diff --git a/changelog.d/14991.misc b/changelog.d/14991.misc
new file mode 100644
index 0000000000..93ceaeafc9
--- /dev/null
+++ b/changelog.d/14991.misc
@@ -0,0 +1 @@
+Improve type hints.
diff --git a/mypy.ini b/mypy.ini
index 22f0911454..2f8806e1f4 100644
--- a/mypy.ini
+++ b/mypy.ini
@@ -32,8 +32,6 @@ exclude = (?x)
    |synapse/storage/databases/main/cache.py
    |synapse/storage/schema/
 
-   |tests/federation/test_federation_catch_up.py
-   |tests/federation/test_federation_sender.py
    |tests/http/federation/test_matrix_federation_agent.py
    |tests/http/federation/test_srv_resolver.py
    |tests/http/test_proxyagent.py
@@ -89,7 +87,7 @@ disallow_untyped_defs = True
 [mypy-tests.events.*]
 disallow_untyped_defs = True
 
-[mypy-tests.federation.transport.test_client]
+[mypy-tests.federation.*]
 disallow_untyped_defs = True
 
 [mypy-tests.handlers.*]
diff --git a/tests/federation/test_complexity.py b/tests/federation/test_complexity.py
index 9f1115dd23..d667dd27bf 100644
--- a/tests/federation/test_complexity.py
+++ b/tests/federation/test_complexity.py
@@ -17,7 +17,7 @@ from unittest.mock import Mock
 from synapse.api.errors import Codes, SynapseError
 from synapse.rest import admin
 from synapse.rest.client import login, room
-from synapse.types import UserID
+from synapse.types import JsonDict, UserID
 
 from tests import unittest
 from tests.test_utils import make_awaitable
@@ -31,12 +31,12 @@ class RoomComplexityTests(unittest.FederatingHomeserverTestCase):
         login.register_servlets,
     ]
 
-    def default_config(self):
+    def default_config(self) -> JsonDict:
         config = super().default_config()
         config["limit_remote_rooms"] = {"enabled": True, "complexity": 0.05}
         return config
 
-    def test_complexity_simple(self):
+    def test_complexity_simple(self) -> None:
 
         u1 = self.register_user("u1", "pass")
         u1_token = self.login("u1", "pass")
@@ -66,7 +66,7 @@ class RoomComplexityTests(unittest.FederatingHomeserverTestCase):
         complexity = channel.json_body["v1"]
         self.assertEqual(complexity, 1.23)
 
-    def test_join_too_large(self):
+    def test_join_too_large(self) -> None:
 
         u1 = self.register_user("u1", "pass")
 
@@ -95,7 +95,7 @@ class RoomComplexityTests(unittest.FederatingHomeserverTestCase):
         self.assertEqual(f.value.code, 400, f.value)
         self.assertEqual(f.value.errcode, Codes.RESOURCE_LIMIT_EXCEEDED)
 
-    def test_join_too_large_admin(self):
+    def test_join_too_large_admin(self) -> None:
         # Check whether an admin can join if option "admins_can_join" is undefined,
         # this option defaults to false, so the join should fail.
 
@@ -126,7 +126,7 @@ class RoomComplexityTests(unittest.FederatingHomeserverTestCase):
         self.assertEqual(f.value.code, 400, f.value)
         self.assertEqual(f.value.errcode, Codes.RESOURCE_LIMIT_EXCEEDED)
 
-    def test_join_too_large_once_joined(self):
+    def test_join_too_large_once_joined(self) -> None:
 
         u1 = self.register_user("u1", "pass")
         u1_token = self.login("u1", "pass")
@@ -180,7 +180,7 @@ class RoomComplexityAdminTests(unittest.FederatingHomeserverTestCase):
         login.register_servlets,
     ]
 
-    def default_config(self):
+    def default_config(self) -> JsonDict:
         config = super().default_config()
         config["limit_remote_rooms"] = {
             "enabled": True,
@@ -189,7 +189,7 @@ class RoomComplexityAdminTests(unittest.FederatingHomeserverTestCase):
         }
         return config
 
-    def test_join_too_large_no_admin(self):
+    def test_join_too_large_no_admin(self) -> None:
         # A user which is not an admin should not be able to join a remote room
         # which is too complex.
 
@@ -220,7 +220,7 @@ class RoomComplexityAdminTests(unittest.FederatingHomeserverTestCase):
         self.assertEqual(f.value.code, 400, f.value)
         self.assertEqual(f.value.errcode, Codes.RESOURCE_LIMIT_EXCEEDED)
 
-    def test_join_too_large_admin(self):
+    def test_join_too_large_admin(self) -> None:
         # An admin should be able to join rooms where a complexity check fails.
 
         u1 = self.register_user("u1", "pass", admin=True)
diff --git a/tests/federation/test_federation_catch_up.py b/tests/federation/test_federation_catch_up.py
index b8fee72898..a986b15f0a 100644
--- a/tests/federation/test_federation_catch_up.py
+++ b/tests/federation/test_federation_catch_up.py
@@ -1,13 +1,17 @@
-from typing import List, Tuple
+from typing import Callable, List, Optional, Tuple
 from unittest.mock import Mock
 
+from twisted.test.proto_helpers import MemoryReactor
+
 from synapse.api.constants import EventTypes
 from synapse.events import EventBase
 from synapse.federation.sender import PerDestinationQueue, TransactionManager
-from synapse.federation.units import Edu
+from synapse.federation.units import Edu, Transaction
 from synapse.rest import admin
 from synapse.rest.client import login, room
+from synapse.server import HomeServer
 from synapse.types import JsonDict
+from synapse.util import Clock
 from synapse.util.retryutils import NotRetryingDestination
 
 from tests.test_utils import event_injection, make_awaitable
@@ -28,23 +32,25 @@ class FederationCatchUpTestCases(FederatingHomeserverTestCase):
         login.register_servlets,
     ]
 
-    def make_homeserver(self, reactor, clock):
+    def make_homeserver(self, reactor: MemoryReactor, clock: Clock) -> HomeServer:
         return self.setup_test_homeserver(
             federation_transport_client=Mock(spec=["send_transaction"]),
         )
 
-    def prepare(self, reactor, clock, hs):
+    def prepare(self, reactor: MemoryReactor, clock: Clock, hs: HomeServer) -> None:
         # stub out get_current_hosts_in_room
-        state_handler = hs.get_state_handler()
+        state_storage_controller = hs.get_storage_controllers().state
 
         # This mock is crucial for destination_rooms to be populated.
-        state_handler.get_current_hosts_in_room = Mock(
-            return_value=make_awaitable(["test", "host2"])
+        # TODO: this seems to no longer be the case---tests pass with this mock
+        # commented out.
+        state_storage_controller.get_current_hosts_in_room = Mock(  # type: ignore[assignment]
+            return_value=make_awaitable({"test", "host2"})
         )
 
         # whenever send_transaction is called, record the pdu data
-        self.pdus = []
-        self.failed_pdus = []
+        self.pdus: List[JsonDict] = []
+        self.failed_pdus: List[JsonDict] = []
         self.is_online = True
         self.hs.get_federation_transport_client().send_transaction.side_effect = (
             self.record_transaction
@@ -55,8 +61,13 @@ class FederationCatchUpTestCases(FederatingHomeserverTestCase):
         config["federation_sender_instances"] = None
         return config
 
-    async def record_transaction(self, txn, json_cb):
-        if self.is_online:
+    async def record_transaction(
+        self, txn: Transaction, json_cb: Optional[Callable[[], JsonDict]]
+    ) -> JsonDict:
+        if json_cb is None:
+            # The tests seem to expect that this method raises in this situation.
+            raise Exception("Blank json_cb")
+        elif self.is_online:
             data = json_cb()
             self.pdus.extend(data["pdus"])
             return {}
@@ -92,7 +103,7 @@ class FederationCatchUpTestCases(FederatingHomeserverTestCase):
         )[0]
         return {"event_id": event_id, "stream_ordering": stream_ordering}
 
-    def test_catch_up_destination_rooms_tracking(self):
+    def test_catch_up_destination_rooms_tracking(self) -> None:
         """
         Tests that we populate the `destination_rooms` table as needed.
         """
@@ -117,7 +128,7 @@ class FederationCatchUpTestCases(FederatingHomeserverTestCase):
         self.assertEqual(row_2["event_id"], event_id_2)
         self.assertEqual(row_1["stream_ordering"], row_2["stream_ordering"] - 1)
 
-    def test_catch_up_last_successful_stream_ordering_tracking(self):
+    def test_catch_up_last_successful_stream_ordering_tracking(self) -> None:
         """
         Tests that we populate the `destination_rooms` table as needed.
         """
@@ -174,7 +185,7 @@ class FederationCatchUpTestCases(FederatingHomeserverTestCase):
             "Send succeeded but not marked as last_successful_stream_ordering",
         )
 
-    def test_catch_up_from_blank_state(self):
+    def test_catch_up_from_blank_state(self) -> None:
         """
         Runs an overall test of federation catch-up from scratch.
         Further tests will focus on more narrow aspects and edge-cases, but I
@@ -261,16 +272,15 @@ class FederationCatchUpTestCases(FederatingHomeserverTestCase):
             destination_tm: str,
             pending_pdus: List[EventBase],
             _pending_edus: List[Edu],
-        ) -> bool:
+        ) -> None:
             assert destination == destination_tm
             results_list.extend(pending_pdus)
-            return True  # success!
 
-        transaction_manager.send_new_transaction = fake_send
+        transaction_manager.send_new_transaction = fake_send  # type: ignore[assignment]
 
         return per_dest_queue, results_list
 
-    def test_catch_up_loop(self):
+    def test_catch_up_loop(self) -> None:
         """
         Tests the behaviour of _catch_up_transmission_loop.
         """
@@ -334,7 +344,7 @@ class FederationCatchUpTestCases(FederatingHomeserverTestCase):
             event_5.internal_metadata.stream_ordering,
         )
 
-    def test_catch_up_on_synapse_startup(self):
+    def test_catch_up_on_synapse_startup(self) -> None:
         """
         Tests the behaviour of get_catch_up_outstanding_destinations and
             _wake_destinations_needing_catchup.
@@ -412,7 +422,7 @@ class FederationCatchUpTestCases(FederatingHomeserverTestCase):
         # patch wake_destination to just count the destinations instead
         woken = []
 
-        def wake_destination_track(destination):
+        def wake_destination_track(destination: str) -> None:
             woken.append(destination)
 
         self.hs.get_federation_sender().wake_destination = wake_destination_track
@@ -432,7 +442,7 @@ class FederationCatchUpTestCases(FederatingHomeserverTestCase):
         # - all destinations are woken exactly once; they appear once in woken.
         self.assertCountEqual(woken, server_names[:-1])
 
-    def test_not_latest_event(self):
+    def test_not_latest_event(self) -> None:
         """Test that we send the latest event in the room even if its not ours."""
 
         per_dest_queue, sent_pdus = self.make_fake_destination_queue()
diff --git a/tests/federation/test_federation_client.py b/tests/federation/test_federation_client.py
index e67f405826..86e1236501 100644
--- a/tests/federation/test_federation_client.py
+++ b/tests/federation/test_federation_client.py
@@ -36,7 +36,9 @@ class FederationClientTest(FederatingHomeserverTestCase):
         login.register_servlets,
     ]
 
-    def prepare(self, reactor: MemoryReactor, clock: Clock, homeserver: HomeServer):
+    def prepare(
+        self, reactor: MemoryReactor, clock: Clock, homeserver: HomeServer
+    ) -> None:
         super().prepare(reactor, clock, homeserver)
 
         # mock out the Agent used by the federation client, which is easier than
@@ -51,7 +53,7 @@ class FederationClientTest(FederatingHomeserverTestCase):
         self.creator = f"@creator:{self.OTHER_SERVER_NAME}"
         self.test_room_id = "!room_id"
 
-    def test_get_room_state(self):
+    def test_get_room_state(self) -> None:
         # mock up some events to use in the response.
         # In real life, these would have things in `prev_events` and `auth_events`, but that's
         # a bit annoying to mock up, and the code under test doesn't care, so we don't bother.
@@ -140,7 +142,7 @@ class FederationClientTest(FederatingHomeserverTestCase):
             ["m.room.create", "m.room.member", "m.room.power_levels"],
         )
 
-    def test_get_pdu_returns_nothing_when_event_does_not_exist(self):
+    def test_get_pdu_returns_nothing_when_event_does_not_exist(self) -> None:
         """No event should be returned when the event does not exist"""
         pulled_pdu_info = self.get_success(
             self.hs.get_federation_client().get_pdu(
@@ -151,11 +153,11 @@ class FederationClientTest(FederatingHomeserverTestCase):
         )
         self.assertEqual(pulled_pdu_info, None)
 
-    def test_get_pdu(self):
+    def test_get_pdu(self) -> None:
         """Test to make sure an event is returned by `get_pdu()`"""
         self._get_pdu_once()
 
-    def test_get_pdu_event_from_cache_is_pristine(self):
+    def test_get_pdu_event_from_cache_is_pristine(self) -> None:
         """Test that modifications made to events returned by `get_pdu()`
         do not propagate back to to the internal cache (events returned should
         be a copy).
diff --git a/tests/federation/test_federation_sender.py b/tests/federation/test_federation_sender.py
index 8692d8190f..ddeffe1ad5 100644
--- a/tests/federation/test_federation_sender.py
+++ b/tests/federation/test_federation_sender.py
@@ -11,18 +11,22 @@
 # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 # See the License for the specific language governing permissions and
 # limitations under the License.
-from typing import Optional
+from typing import Callable, FrozenSet, List, Optional, Set
 from unittest.mock import Mock
 
 from signedjson import key, sign
 from signedjson.types import BaseKey, SigningKey
 
 from twisted.internet import defer
+from twisted.test.proto_helpers import MemoryReactor
 
 from synapse.api.constants import EduTypes, RoomEncryptionAlgorithms
+from synapse.federation.units import Transaction
 from synapse.rest import admin
 from synapse.rest.client import login
+from synapse.server import HomeServer
 from synapse.types import JsonDict, ReadReceipt
+from synapse.util import Clock
 
 from tests.test_utils import make_awaitable
 from tests.unittest import HomeserverTestCase
@@ -36,16 +40,16 @@ class FederationSenderReceiptsTestCases(HomeserverTestCase):
     re-enabled for the main process.
     """
 
-    def make_homeserver(self, reactor, clock):
+    def make_homeserver(self, reactor: MemoryReactor, clock: Clock) -> HomeServer:
         hs = self.setup_test_homeserver(
             federation_transport_client=Mock(spec=["send_transaction"]),
         )
 
-        hs.get_storage_controllers().state.get_current_hosts_in_room = Mock(
+        hs.get_storage_controllers().state.get_current_hosts_in_room = Mock(  # type: ignore[assignment]
             return_value=make_awaitable({"test", "host2"})
         )
 
-        hs.get_storage_controllers().state.get_current_hosts_in_room_or_partial_state_approximation = (
+        hs.get_storage_controllers().state.get_current_hosts_in_room_or_partial_state_approximation = (  # type: ignore[assignment]
             hs.get_storage_controllers().state.get_current_hosts_in_room
         )
 
@@ -56,7 +60,7 @@ class FederationSenderReceiptsTestCases(HomeserverTestCase):
         config["federation_sender_instances"] = None
         return config
 
-    def test_send_receipts(self):
+    def test_send_receipts(self) -> None:
         mock_send_transaction = (
             self.hs.get_federation_transport_client().send_transaction
         )
@@ -98,7 +102,7 @@ class FederationSenderReceiptsTestCases(HomeserverTestCase):
             ],
         )
 
-    def test_send_receipts_thread(self):
+    def test_send_receipts_thread(self) -> None:
         mock_send_transaction = (
             self.hs.get_federation_transport_client().send_transaction
         )
@@ -174,7 +178,7 @@ class FederationSenderReceiptsTestCases(HomeserverTestCase):
             ],
         )
 
-    def test_send_receipts_with_backoff(self):
+    def test_send_receipts_with_backoff(self) -> None:
         """Send two receipts in quick succession; the second should be flushed, but
         only after 20ms"""
         mock_send_transaction = (
@@ -272,51 +276,55 @@ class FederationSenderDevicesTestCases(HomeserverTestCase):
         login.register_servlets,
     ]
 
-    def make_homeserver(self, reactor, clock):
+    def make_homeserver(self, reactor: MemoryReactor, clock: Clock) -> HomeServer:
         return self.setup_test_homeserver(
             federation_transport_client=Mock(
                 spec=["send_transaction", "query_user_devices"]
             ),
         )
 
-    def default_config(self):
+    def default_config(self) -> JsonDict:
         c = super().default_config()
         # Enable federation sending on the main process.
         c["federation_sender_instances"] = None
         return c
 
-    def prepare(self, reactor, clock, hs):
+    def prepare(self, reactor: MemoryReactor, clock: Clock, hs: HomeServer) -> None:
         test_room_id = "!room:host1"
 
         # stub out `get_rooms_for_user` and `get_current_hosts_in_room` so that the
         # server thinks the user shares a room with `@user2:host2`
-        def get_rooms_for_user(user_id):
-            return defer.succeed({test_room_id})
+        def get_rooms_for_user(user_id: str) -> "defer.Deferred[FrozenSet[str]]":
+            return defer.succeed(frozenset({test_room_id}))
 
-        hs.get_datastores().main.get_rooms_for_user = get_rooms_for_user
+        hs.get_datastores().main.get_rooms_for_user = get_rooms_for_user  # type: ignore[assignment]
 
-        async def get_current_hosts_in_room(room_id):
+        async def get_current_hosts_in_room(room_id: str) -> Set[str]:
             if room_id == test_room_id:
-                return ["host2"]
+                return {"host2"}
+            else:
+                # TODO: We should fail the test when we encounter an unxpected room ID.
+                # We can't just use `self.fail(...)` here because the app code is greedy
+                # with `Exception` and will catch it before the test can see it.
+                return set()
 
-            # TODO: We should fail the test when we encounter an unxpected room ID.
-            # We can't just use `self.fail(...)` here because the app code is greedy
-            # with `Exception` and will catch it before the test can see it.
-
-        hs.get_datastores().main.get_current_hosts_in_room = get_current_hosts_in_room
+        hs.get_datastores().main.get_current_hosts_in_room = get_current_hosts_in_room  # type: ignore[assignment]
 
         # whenever send_transaction is called, record the edu data
-        self.edus = []
+        self.edus: List[JsonDict] = []
         self.hs.get_federation_transport_client().send_transaction.side_effect = (
             self.record_transaction
         )
 
-    def record_transaction(self, txn, json_cb):
+    def record_transaction(
+        self, txn: Transaction, json_cb: Optional[Callable[[], JsonDict]] = None
+    ) -> "defer.Deferred[JsonDict]":
+        assert json_cb is not None
         data = json_cb()
         self.edus.extend(data["edus"])
         return defer.succeed({})
 
-    def test_send_device_updates(self):
+    def test_send_device_updates(self) -> None:
         """Basic case: each device update should result in an EDU"""
         # create a device
         u1 = self.register_user("user", "pass")
@@ -340,7 +348,7 @@ class FederationSenderDevicesTestCases(HomeserverTestCase):
         self.assertEqual(len(self.edus), 1)
         self.check_device_update_edu(self.edus.pop(0), u1, "D2", stream_id)
 
-    def test_dont_send_device_updates_for_remote_users(self):
+    def test_dont_send_device_updates_for_remote_users(self) -> None:
         """Check that we don't send device updates for remote users"""
 
         # Send the server a device list EDU for the other user, this will cause
@@ -379,7 +387,7 @@ class FederationSenderDevicesTestCases(HomeserverTestCase):
         )
         self.assertIn("D1", devices)
 
-    def test_upload_signatures(self):
+    def test_upload_signatures(self) -> None:
         """Uploading signatures on some devices should produce updates for that user"""
 
         e2e_handler = self.hs.get_e2e_keys_handler()
@@ -391,7 +399,7 @@ class FederationSenderDevicesTestCases(HomeserverTestCase):
 
         # expect two edus
         self.assertEqual(len(self.edus), 2)
-        stream_id = None
+        stream_id: Optional[int] = None
         stream_id = self.check_device_update_edu(self.edus.pop(0), u1, "D1", stream_id)
         stream_id = self.check_device_update_edu(self.edus.pop(0), u1, "D2", stream_id)
 
@@ -473,13 +481,13 @@ class FederationSenderDevicesTestCases(HomeserverTestCase):
             self.assertEqual(edu["edu_type"], EduTypes.DEVICE_LIST_UPDATE)
             c = edu["content"]
             if stream_id is not None:
-                self.assertEqual(c["prev_id"], [stream_id])
+                self.assertEqual(c["prev_id"], [stream_id])  # type: ignore[unreachable]
                 self.assertGreaterEqual(c["stream_id"], stream_id)
             stream_id = c["stream_id"]
         devices = {edu["content"]["device_id"] for edu in self.edus}
         self.assertEqual({"D1", "D2"}, devices)
 
-    def test_delete_devices(self):
+    def test_delete_devices(self) -> None:
         """If devices are deleted, that should result in EDUs too"""
 
         # create devices
@@ -521,7 +529,7 @@ class FederationSenderDevicesTestCases(HomeserverTestCase):
         devices = {edu["content"]["device_id"] for edu in self.edus}
         self.assertEqual({"D1", "D2", "D3"}, devices)
 
-    def test_unreachable_server(self):
+    def test_unreachable_server(self) -> None:
         """If the destination server is unreachable, all the updates should get sent on
         recovery
         """
@@ -555,7 +563,7 @@ class FederationSenderDevicesTestCases(HomeserverTestCase):
 
         # for each device, there should be a single update
         self.assertEqual(len(self.edus), 3)
-        stream_id = None
+        stream_id: Optional[int] = None
         for edu in self.edus:
             self.assertEqual(edu["edu_type"], EduTypes.DEVICE_LIST_UPDATE)
             c = edu["content"]
@@ -566,7 +574,7 @@ class FederationSenderDevicesTestCases(HomeserverTestCase):
         devices = {edu["content"]["device_id"] for edu in self.edus}
         self.assertEqual({"D1", "D2", "D3"}, devices)
 
-    def test_prune_outbound_device_pokes1(self):
+    def test_prune_outbound_device_pokes1(self) -> None:
         """If a destination is unreachable, and the updates are pruned, we should get
         a single update.
 
@@ -615,7 +623,7 @@ class FederationSenderDevicesTestCases(HomeserverTestCase):
         # synapse uses an empty prev_id list to indicate "needs a full resync".
         self.assertEqual(c["prev_id"], [])
 
-    def test_prune_outbound_device_pokes2(self):
+    def test_prune_outbound_device_pokes2(self) -> None:
         """If a destination is unreachable, and the updates are pruned, we should get
         a single update.
 
@@ -741,7 +749,7 @@ def encode_pubkey(sk: SigningKey) -> str:
     return key.encode_verify_key_base64(key.get_verify_key(sk))
 
 
-def build_device_dict(user_id: str, device_id: str, sk: SigningKey):
+def build_device_dict(user_id: str, device_id: str, sk: SigningKey) -> JsonDict:
     """Build a dict representing the given device"""
     return {
         "user_id": user_id,
diff --git a/tests/federation/test_federation_server.py b/tests/federation/test_federation_server.py
index be719e49c0..bba6469b55 100644
--- a/tests/federation/test_federation_server.py
+++ b/tests/federation/test_federation_server.py
@@ -21,7 +21,7 @@ from twisted.test.proto_helpers import MemoryReactor
 
 from synapse.api.room_versions import KNOWN_ROOM_VERSIONS
 from synapse.config.server import DEFAULT_ROOM_VERSION
-from synapse.events import make_event_from_dict
+from synapse.events import EventBase, make_event_from_dict
 from synapse.federation.federation_server import server_matches_acl_event
 from synapse.rest import admin
 from synapse.rest.client import login, room
@@ -42,7 +42,7 @@ class FederationServerTests(unittest.FederatingHomeserverTestCase):
     ]
 
     @parameterized.expand([(b"",), (b"foo",), (b'{"limit": Infinity}',)])
-    def test_bad_request(self, query_content):
+    def test_bad_request(self, query_content: bytes) -> None:
         """
         Querying with bad data returns a reasonable error code.
         """
@@ -64,7 +64,7 @@ class FederationServerTests(unittest.FederatingHomeserverTestCase):
 
 
 class ServerACLsTestCase(unittest.TestCase):
-    def test_blacklisted_server(self):
+    def test_blacklisted_server(self) -> None:
         e = _create_acl_event({"allow": ["*"], "deny": ["evil.com"]})
         logging.info("ACL event: %s", e.content)
 
@@ -74,7 +74,7 @@ class ServerACLsTestCase(unittest.TestCase):
         self.assertTrue(server_matches_acl_event("evil.com.au", e))
         self.assertTrue(server_matches_acl_event("honestly.not.evil.com", e))
 
-    def test_block_ip_literals(self):
+    def test_block_ip_literals(self) -> None:
         e = _create_acl_event({"allow_ip_literals": False, "allow": ["*"]})
         logging.info("ACL event: %s", e.content)
 
@@ -83,7 +83,7 @@ class ServerACLsTestCase(unittest.TestCase):
         self.assertFalse(server_matches_acl_event("[1:2::]", e))
         self.assertTrue(server_matches_acl_event("1:2:3:4", e))
 
-    def test_wildcard_matching(self):
+    def test_wildcard_matching(self) -> None:
         e = _create_acl_event({"allow": ["good*.com"]})
         self.assertTrue(
             server_matches_acl_event("good.com", e),
@@ -110,7 +110,7 @@ class StateQueryTests(unittest.FederatingHomeserverTestCase):
         login.register_servlets,
     ]
 
-    def test_needs_to_be_in_room(self):
+    def test_needs_to_be_in_room(self) -> None:
         """/v1/state/<room_id> requires the server to be in the room"""
         u1 = self.register_user("u1", "pass")
         u1_token = self.login("u1", "pass")
@@ -131,7 +131,7 @@ class SendJoinFederationTests(unittest.FederatingHomeserverTestCase):
         login.register_servlets,
     ]
 
-    def prepare(self, reactor: MemoryReactor, clock: Clock, hs: HomeServer):
+    def prepare(self, reactor: MemoryReactor, clock: Clock, hs: HomeServer) -> None:
         super().prepare(reactor, clock, hs)
 
         self._storage_controllers = hs.get_storage_controllers()
@@ -157,7 +157,7 @@ class SendJoinFederationTests(unittest.FederatingHomeserverTestCase):
         self.assertEqual(channel.code, HTTPStatus.OK, channel.json_body)
         return channel.json_body
 
-    def test_send_join(self):
+    def test_send_join(self) -> None:
         """happy-path test of send_join"""
         joining_user = "@misspiggy:" + self.OTHER_SERVER_NAME
         join_result = self._make_join(joining_user)
@@ -324,7 +324,7 @@ class SendJoinFederationTests(unittest.FederatingHomeserverTestCase):
     #   is probably sufficient to reassure that the bucket is updated.
 
 
-def _create_acl_event(content):
+def _create_acl_event(content: JsonDict) -> EventBase:
     return make_event_from_dict(
         {
             "room_id": "!a:b",
diff --git a/tests/federation/transport/server/test__base.py b/tests/federation/transport/server/test__base.py
index e88e5d8bb3..55655de862 100644
--- a/tests/federation/transport/server/test__base.py
+++ b/tests/federation/transport/server/test__base.py
@@ -15,6 +15,8 @@
 from http import HTTPStatus
 from typing import Dict, List, Tuple
 
+from twisted.web.resource import Resource
+
 from synapse.api.errors import Codes
 from synapse.federation.transport.server import BaseFederationServlet
 from synapse.federation.transport.server._base import Authenticator, _parse_auth_header
@@ -62,7 +64,7 @@ class BaseFederationServletCancellationTests(unittest.FederatingHomeserverTestCa
 
     path = f"{CancellableFederationServlet.PREFIX}{CancellableFederationServlet.PATH}"
 
-    def create_test_resource(self):
+    def create_test_resource(self) -> Resource:
         """Overrides `HomeserverTestCase.create_test_resource`."""
         resource = JsonResource(self.hs)
 
diff --git a/tests/federation/transport/test_knocking.py b/tests/federation/transport/test_knocking.py
index ff589c0b6c..70209ab090 100644
--- a/tests/federation/transport/test_knocking.py
+++ b/tests/federation/transport/test_knocking.py
@@ -12,15 +12,19 @@
 # See the License for the specific language governing permissions and
 # limitations under the License.
 from collections import OrderedDict
-from typing import Dict, List
+from typing import Any, Dict, List, Optional
+
+from twisted.test.proto_helpers import MemoryReactor
 
 from synapse.api.constants import EventTypes, JoinRules, Membership
-from synapse.api.room_versions import RoomVersions
-from synapse.events import builder
+from synapse.api.room_versions import RoomVersion, RoomVersions
+from synapse.events import EventBase, builder
+from synapse.events.snapshot import EventContext
 from synapse.rest import admin
 from synapse.rest.client import login, room
 from synapse.server import HomeServer
 from synapse.types import RoomAlias
+from synapse.util import Clock
 
 from tests.test_utils import event_injection
 from tests.unittest import FederatingHomeserverTestCase, HomeserverTestCase
@@ -197,7 +201,9 @@ class FederationKnockingTestCase(
         login.register_servlets,
     ]
 
-    def prepare(self, reactor, clock, homeserver):
+    def prepare(
+        self, reactor: MemoryReactor, clock: Clock, homeserver: HomeServer
+    ) -> None:
         self.store = homeserver.get_datastores().main
 
         # We're not going to be properly signing events as our remote homeserver is fake,
@@ -205,23 +211,29 @@ class FederationKnockingTestCase(
         # Note that these checks are not relevant to this test case.
 
         # Have this homeserver auto-approve all event signature checking.
-        async def approve_all_signature_checking(_, pdu):
+        async def approve_all_signature_checking(
+            room_version: RoomVersion,
+            pdu: EventBase,
+            record_failure_callback: Any = None,
+        ) -> EventBase:
             return pdu
 
-        homeserver.get_federation_server()._check_sigs_and_hash = (
+        homeserver.get_federation_server()._check_sigs_and_hash = (  # type: ignore[assignment]
             approve_all_signature_checking
         )
 
         # Have this homeserver skip event auth checks. This is necessary due to
         # event auth checks ensuring that events were signed by the sender's homeserver.
-        async def _check_event_auth(origin, event, context, *args, **kwargs):
-            return context
+        async def _check_event_auth(
+            origin: Optional[str], event: EventBase, context: EventContext
+        ) -> None:
+            pass
 
-        homeserver.get_federation_event_handler()._check_event_auth = _check_event_auth
+        homeserver.get_federation_event_handler()._check_event_auth = _check_event_auth  # type: ignore[assignment]
 
         return super().prepare(reactor, clock, homeserver)
 
-    def test_room_state_returned_when_knocking(self):
+    def test_room_state_returned_when_knocking(self) -> None:
         """
         Tests that specific, stripped state events from a room are returned after
         a remote homeserver successfully knocks on a local room.
diff --git a/tests/federation/transport/test_server.py b/tests/federation/transport/test_server.py
index cfd550a04b..c4231f4aa9 100644
--- a/tests/federation/transport/test_server.py
+++ b/tests/federation/transport/test_server.py
@@ -20,7 +20,7 @@ from tests.unittest import DEBUG, override_config
 
 class RoomDirectoryFederationTests(unittest.FederatingHomeserverTestCase):
     @override_config({"allow_public_rooms_over_federation": False})
-    def test_blocked_public_room_list_over_federation(self):
+    def test_blocked_public_room_list_over_federation(self) -> None:
         """Test that unauthenticated requests to the public rooms directory 403 when
         allow_public_rooms_over_federation is False.
         """
@@ -31,7 +31,7 @@ class RoomDirectoryFederationTests(unittest.FederatingHomeserverTestCase):
         self.assertEqual(403, channel.code)
 
     @override_config({"allow_public_rooms_over_federation": True})
-    def test_open_public_room_list_over_federation(self):
+    def test_open_public_room_list_over_federation(self) -> None:
         """Test that unauthenticated requests to the public rooms directory 200 when
         allow_public_rooms_over_federation is True.
         """
@@ -42,7 +42,7 @@ class RoomDirectoryFederationTests(unittest.FederatingHomeserverTestCase):
         self.assertEqual(200, channel.code)
 
     @DEBUG
-    def test_edu_debugging_doesnt_explode(self):
+    def test_edu_debugging_doesnt_explode(self) -> None:
         """Sanity check incoming federation succeeds with `synapse.debug_8631` enabled.
 
         Remove this when we strip out issue_8631_logger.