diff --git a/changelog.d/7945.misc b/changelog.d/7945.misc
new file mode 100644
index 0000000000..da612fd576
--- /dev/null
+++ b/changelog.d/7945.misc
@@ -0,0 +1 @@
+Update comments that refer to Deferreds for async functions.
diff --git a/synapse/handlers/admin.py b/synapse/handlers/admin.py
index f3c0aeceb6..506bb2b275 100644
--- a/synapse/handlers/admin.py
+++ b/synapse/handlers/admin.py
@@ -72,7 +72,7 @@ class AdminHandler(BaseHandler):
             writer (ExfiltrationWriter)
 
         Returns:
-            defer.Deferred: Resolves when all data for a user has been written.
+            Resolves when all data for a user has been written.
             The returned value is that returned by `writer.finished()`.
         """
         # Get all rooms the user is in or has been in
diff --git a/synapse/handlers/e2e_keys.py b/synapse/handlers/e2e_keys.py
index 361dd64cd2..84169c1022 100644
--- a/synapse/handlers/e2e_keys.py
+++ b/synapse/handlers/e2e_keys.py
@@ -16,10 +16,11 @@
 # limitations under the License.
 
 import logging
+from typing import Dict, List, Optional, Tuple
 
 import attr
 from canonicaljson import encode_canonical_json, json
-from signedjson.key import decode_verify_key_bytes
+from signedjson.key import VerifyKey, decode_verify_key_bytes
 from signedjson.sign import SignatureVerifyException, verify_signed_json
 from unpaddedbase64 import decode_base64
 
@@ -265,7 +266,9 @@ class E2eKeysHandler(object):
 
         return ret
 
-    async def get_cross_signing_keys_from_cache(self, query, from_user_id):
+    async def get_cross_signing_keys_from_cache(
+        self, query, from_user_id
+    ) -> Dict[str, Dict[str, dict]]:
         """Get cross-signing keys for users from the database
 
         Args:
@@ -277,8 +280,7 @@ class E2eKeysHandler(object):
                 can see.
 
         Returns:
-            defer.Deferred[dict[str, dict[str, dict]]]: map from
-                (master_keys|self_signing_keys|user_signing_keys) -> user_id -> key
+            A map from (master_keys|self_signing_keys|user_signing_keys) -> user_id -> key
         """
         master_keys = {}
         self_signing_keys = {}
@@ -312,16 +314,17 @@ class E2eKeysHandler(object):
         }
 
     @trace
-    async def query_local_devices(self, query):
+    async def query_local_devices(
+        self, query: Dict[str, Optional[List[str]]]
+    ) -> Dict[str, Dict[str, dict]]:
         """Get E2E device keys for local users
 
         Args:
-            query (dict[string, list[string]|None): map from user_id to a list
+            query: map from user_id to a list
                  of devices to query (None for all devices)
 
         Returns:
-            defer.Deferred: (resolves to dict[string, dict[string, dict]]):
-                 map from user_id -> device_id -> device details
+            A map from user_id -> device_id -> device details
         """
         set_tag("local_query", query)
         local_query = []
@@ -1004,7 +1007,7 @@ class E2eKeysHandler(object):
 
     async def _retrieve_cross_signing_keys_for_remote_user(
         self, user: UserID, desired_key_type: str,
-    ):
+    ) -> Tuple[Optional[dict], Optional[str], Optional[VerifyKey]]:
         """Queries cross-signing keys for a remote user and saves them to the database
 
         Only the key specified by `key_type` will be returned, while all retrieved keys
@@ -1015,8 +1018,7 @@ class E2eKeysHandler(object):
             desired_key_type: The type of key to receive. One of "master", "self_signing"
 
         Returns:
-            Deferred[Tuple[Optional[Dict], Optional[str], Optional[VerifyKey]]]: A tuple
-            of the retrieved key content, the key's ID and the matching VerifyKey.
+            A tuple of the retrieved key content, the key's ID and the matching VerifyKey.
             If the key cannot be retrieved, all values in the tuple will instead be None.
         """
         try:
diff --git a/synapse/handlers/federation.py b/synapse/handlers/federation.py
index 71ac5dca99..758ffdf01d 100644
--- a/synapse/handlers/federation.py
+++ b/synapse/handlers/federation.py
@@ -1394,7 +1394,7 @@ class FederationHandler(BaseHandler):
             # it's just a best-effort thing at this point. We do want to do
             # them roughly in order, though, otherwise we'll end up making
             # lots of requests for missing prev_events which we do actually
-            # have. Hence we fire off the deferred, but don't wait for it.
+            # have. Hence we fire off the background task, but don't wait for it.
 
             run_in_background(self._handle_queued_pdus, room_queue)
 
@@ -2994,7 +2994,9 @@ class FederationHandler(BaseHandler):
         else:
             user_joined_room(self.distributor, user, room_id)
 
-    async def get_room_complexity(self, remote_room_hosts, room_id):
+    async def get_room_complexity(
+        self, remote_room_hosts: List[str], room_id: str
+    ) -> Optional[dict]:
         """
         Fetch the complexity of a remote room over federation.
 
@@ -3003,7 +3005,7 @@ class FederationHandler(BaseHandler):
             room_id (str): The room ID to ask about.
 
         Returns:
-            Deferred[dict] or Deferred[None]: Dict contains the complexity
+            Dict contains the complexity
             metric versions, while None means we could not fetch the complexity.
         """
 
diff --git a/synapse/handlers/identity.py b/synapse/handlers/identity.py
index 701233ebb4..0bd2c3e37a 100644
--- a/synapse/handlers/identity.py
+++ b/synapse/handlers/identity.py
@@ -19,6 +19,7 @@
 
 import logging
 import urllib.parse
+from typing import Awaitable, Callable, Dict, List, Optional, Tuple
 
 from canonicaljson import json
 from signedjson.key import decode_verify_key_bytes
@@ -36,6 +37,7 @@ from synapse.api.errors import (
 )
 from synapse.config.emailconfig import ThreepidBehaviour
 from synapse.http.client import SimpleHttpClient
+from synapse.types import JsonDict, Requester
 from synapse.util.hash import sha256_and_url_safe_base64
 from synapse.util.stringutils import assert_valid_client_secret, random_string
 
@@ -59,23 +61,23 @@ class IdentityHandler(BaseHandler):
         self.federation_http_client = hs.get_http_client()
         self.hs = hs
 
-    async def threepid_from_creds(self, id_server, creds):
+    async def threepid_from_creds(
+        self, id_server: str, creds: Dict[str, str]
+    ) -> Optional[JsonDict]:
         """
         Retrieve and validate a threepid identifier from a "credentials" dictionary against a
         given identity server
 
         Args:
-            id_server (str): The identity server to validate 3PIDs against. Must be a
+            id_server: The identity server to validate 3PIDs against. Must be a
                 complete URL including the protocol (http(s)://)
-
-            creds (dict[str, str]): Dictionary containing the following keys:
+            creds: Dictionary containing the following keys:
                 * client_secret|clientSecret: A unique secret str provided by the client
                 * sid: The ID of the validation session
 
         Returns:
-            Deferred[dict[str,str|int]|None]: A dictionary consisting of response params to
-                the /getValidated3pid endpoint of the Identity Service API, or None if the
-                threepid was not found
+            A dictionary consisting of response params to the /getValidated3pid
+            endpoint of the Identity Service API, or None if the threepid was not found
         """
         client_secret = creds.get("client_secret") or creds.get("clientSecret")
         if not client_secret:
@@ -119,26 +121,27 @@ class IdentityHandler(BaseHandler):
         return None
 
     async def bind_threepid(
-        self, client_secret, sid, mxid, id_server, id_access_token=None, use_v2=True
-    ):
+        self,
+        client_secret: str,
+        sid: str,
+        mxid: str,
+        id_server: str,
+        id_access_token: Optional[str] = None,
+        use_v2: bool = True,
+    ) -> JsonDict:
         """Bind a 3PID to an identity server
 
         Args:
-            client_secret (str): A unique secret provided by the client
-
-            sid (str): The ID of the validation session
-
-            mxid (str): The MXID to bind the 3PID to
-
-            id_server (str): The domain of the identity server to query
-
-            id_access_token (str): The access token to authenticate to the identity
+            client_secret: A unique secret provided by the client
+            sid: The ID of the validation session
+            mxid: The MXID to bind the 3PID to
+            id_server: The domain of the identity server to query
+            id_access_token: The access token to authenticate to the identity
                 server with, if necessary. Required if use_v2 is true
-
-            use_v2 (bool): Whether to use v2 Identity Service API endpoints. Defaults to True
+            use_v2: Whether to use v2 Identity Service API endpoints. Defaults to True
 
         Returns:
-            Deferred[dict]: The response from the identity server
+            The response from the identity server
         """
         logger.debug("Proxying threepid bind request for %s to %s", mxid, id_server)
 
@@ -151,7 +154,7 @@ class IdentityHandler(BaseHandler):
         bind_data = {"sid": sid, "client_secret": client_secret, "mxid": mxid}
         if use_v2:
             bind_url = "https://%s/_matrix/identity/v2/3pid/bind" % (id_server,)
-            headers["Authorization"] = create_id_access_token_header(id_access_token)
+            headers["Authorization"] = create_id_access_token_header(id_access_token)  # type: ignore
         else:
             bind_url = "https://%s/_matrix/identity/api/v1/3pid/bind" % (id_server,)
 
@@ -187,20 +190,20 @@ class IdentityHandler(BaseHandler):
         )
         return res
 
-    async def try_unbind_threepid(self, mxid, threepid):
+    async def try_unbind_threepid(self, mxid: str, threepid: dict) -> bool:
         """Attempt to remove a 3PID from an identity server, or if one is not provided, all
         identity servers we're aware the binding is present on
 
         Args:
-            mxid (str): Matrix user ID of binding to be removed
-            threepid (dict): Dict with medium & address of binding to be
+            mxid: Matrix user ID of binding to be removed
+            threepid: Dict with medium & address of binding to be
                 removed, and an optional id_server.
 
         Raises:
             SynapseError: If we failed to contact the identity server
 
         Returns:
-            Deferred[bool]: True on success, otherwise False if the identity
+            True on success, otherwise False if the identity
             server doesn't support unbinding (or no identity server found to
             contact).
         """
@@ -223,19 +226,21 @@ class IdentityHandler(BaseHandler):
 
         return changed
 
-    async def try_unbind_threepid_with_id_server(self, mxid, threepid, id_server):
+    async def try_unbind_threepid_with_id_server(
+        self, mxid: str, threepid: dict, id_server: str
+    ) -> bool:
         """Removes a binding from an identity server
 
         Args:
-            mxid (str): Matrix user ID of binding to be removed
-            threepid (dict): Dict with medium & address of binding to be removed
-            id_server (str): Identity server to unbind from
+            mxid: Matrix user ID of binding to be removed
+            threepid: Dict with medium & address of binding to be removed
+            id_server: Identity server to unbind from
 
         Raises:
             SynapseError: If we failed to contact the identity server
 
         Returns:
-            Deferred[bool]: True on success, otherwise False if the identity
+            True on success, otherwise False if the identity
             server doesn't support unbinding
         """
         url = "https://%s/_matrix/identity/api/v1/3pid/unbind" % (id_server,)
@@ -287,23 +292,23 @@ class IdentityHandler(BaseHandler):
 
     async def send_threepid_validation(
         self,
-        email_address,
-        client_secret,
-        send_attempt,
-        send_email_func,
-        next_link=None,
-    ):
+        email_address: str,
+        client_secret: str,
+        send_attempt: int,
+        send_email_func: Callable[[str, str, str, str], Awaitable],
+        next_link: Optional[str] = None,
+    ) -> str:
         """Send a threepid validation email for password reset or
         registration purposes
 
         Args:
-            email_address (str): The user's email address
-            client_secret (str): The provided client secret
-            send_attempt (int): Which send attempt this is
-            send_email_func (func): A function that takes an email address, token,
-                                    client_secret and session_id, sends an email
-                                    and returns a Deferred.
-            next_link (str|None): The URL to redirect the user to after validation
+            email_address: The user's email address
+            client_secret: The provided client secret
+            send_attempt: Which send attempt this is
+            send_email_func: A function that takes an email address, token,
+                             client_secret and session_id, sends an email
+                             and returns an Awaitable.
+            next_link: The URL to redirect the user to after validation
 
         Returns:
             The new session_id upon success
@@ -372,17 +377,22 @@ class IdentityHandler(BaseHandler):
         return session_id
 
     async def requestEmailToken(
-        self, id_server, email, client_secret, send_attempt, next_link=None
-    ):
+        self,
+        id_server: str,
+        email: str,
+        client_secret: str,
+        send_attempt: int,
+        next_link: Optional[str] = None,
+    ) -> JsonDict:
         """
         Request an external server send an email on our behalf for the purposes of threepid
         validation.
 
         Args:
-            id_server (str): The identity server to proxy to
-            email (str): The email to send the message to
-            client_secret (str): The unique client_secret sends by the user
-            send_attempt (int): Which attempt this is
+            id_server: The identity server to proxy to
+            email: The email to send the message to
+            client_secret: The unique client_secret sends by the user
+            send_attempt: Which attempt this is
             next_link: A link to redirect the user to once they submit the token
 
         Returns:
@@ -419,22 +429,22 @@ class IdentityHandler(BaseHandler):
 
     async def requestMsisdnToken(
         self,
-        id_server,
-        country,
-        phone_number,
-        client_secret,
-        send_attempt,
-        next_link=None,
-    ):
+        id_server: str,
+        country: str,
+        phone_number: str,
+        client_secret: str,
+        send_attempt: int,
+        next_link: Optional[str] = None,
+    ) -> JsonDict:
         """
         Request an external server send an SMS message on our behalf for the purposes of
         threepid validation.
         Args:
-            id_server (str): The identity server to proxy to
-            country (str): The country code of the phone number
-            phone_number (str): The number to send the message to
-            client_secret (str): The unique client_secret sends by the user
-            send_attempt (int): Which attempt this is
+            id_server: The identity server to proxy to
+            country: The country code of the phone number
+            phone_number: The number to send the message to
+            client_secret: The unique client_secret sends by the user
+            send_attempt: Which attempt this is
             next_link: A link to redirect the user to once they submit the token
 
         Returns:
@@ -480,17 +490,18 @@ class IdentityHandler(BaseHandler):
         )
         return data
 
-    async def validate_threepid_session(self, client_secret, sid):
+    async def validate_threepid_session(
+        self, client_secret: str, sid: str
+    ) -> Optional[JsonDict]:
         """Validates a threepid session with only the client secret and session ID
         Tries validating against any configured account_threepid_delegates as well as locally.
 
         Args:
-            client_secret (str): A secret provided by the client
-
-            sid (str): The ID of the session
+            client_secret: A secret provided by the client
+            sid: The ID of the session
 
         Returns:
-            Dict[str, str|int] if validation was successful, otherwise None
+            The json response if validation was successful, otherwise None
         """
         # XXX: We shouldn't need to keep wrapping and unwrapping this value
         threepid_creds = {"client_secret": client_secret, "sid": sid}
@@ -523,23 +534,22 @@ class IdentityHandler(BaseHandler):
 
         return validation_session
 
-    async def proxy_msisdn_submit_token(self, id_server, client_secret, sid, token):
+    async def proxy_msisdn_submit_token(
+        self, id_server: str, client_secret: str, sid: str, token: str
+    ) -> JsonDict:
         """Proxy a POST submitToken request to an identity server for verification purposes
 
         Args:
-            id_server (str): The identity server URL to contact
-
-            client_secret (str): Secret provided by the client
-
-            sid (str): The ID of the session
-
-            token (str): The verification token
+            id_server: The identity server URL to contact
+            client_secret: Secret provided by the client
+            sid: The ID of the session
+            token: The verification token
 
         Raises:
             SynapseError: If we failed to contact the identity server
 
         Returns:
-            Deferred[dict]: The response dict from the identity server
+            The response dict from the identity server
         """
         body = {"client_secret": client_secret, "sid": sid, "token": token}
 
@@ -554,19 +564,25 @@ class IdentityHandler(BaseHandler):
             logger.warning("Error contacting msisdn account_threepid_delegate: %s", e)
             raise SynapseError(400, "Error contacting the identity server")
 
-    async def lookup_3pid(self, id_server, medium, address, id_access_token=None):
+    async def lookup_3pid(
+        self,
+        id_server: str,
+        medium: str,
+        address: str,
+        id_access_token: Optional[str] = None,
+    ) -> Optional[str]:
         """Looks up a 3pid in the passed identity server.
 
         Args:
-            id_server (str): The server name (including port, if required)
+            id_server: The server name (including port, if required)
                 of the identity server to use.
-            medium (str): The type of the third party identifier (e.g. "email").
-            address (str): The third party identifier (e.g. "foo@example.com").
-            id_access_token (str|None): The access token to authenticate to the identity
+            medium: The type of the third party identifier (e.g. "email").
+            address: The third party identifier (e.g. "foo@example.com").
+            id_access_token: The access token to authenticate to the identity
                 server with
 
         Returns:
-            str|None: the matrix ID of the 3pid, or None if it is not recognized.
+            the matrix ID of the 3pid, or None if it is not recognized.
         """
         if id_access_token is not None:
             try:
@@ -591,17 +607,19 @@ class IdentityHandler(BaseHandler):
 
         return await self._lookup_3pid_v1(id_server, medium, address)
 
-    async def _lookup_3pid_v1(self, id_server, medium, address):
+    async def _lookup_3pid_v1(
+        self, id_server: str, medium: str, address: str
+    ) -> Optional[str]:
         """Looks up a 3pid in the passed identity server using v1 lookup.
 
         Args:
-            id_server (str): The server name (including port, if required)
+            id_server: The server name (including port, if required)
                 of the identity server to use.
-            medium (str): The type of the third party identifier (e.g. "email").
-            address (str): The third party identifier (e.g. "foo@example.com").
+            medium: The type of the third party identifier (e.g. "email").
+            address: The third party identifier (e.g. "foo@example.com").
 
         Returns:
-            str: the matrix ID of the 3pid, or None if it is not recognized.
+            the matrix ID of the 3pid, or None if it is not recognized.
         """
         try:
             data = await self.blacklisting_http_client.get_json(
@@ -621,18 +639,20 @@ class IdentityHandler(BaseHandler):
 
         return None
 
-    async def _lookup_3pid_v2(self, id_server, id_access_token, medium, address):
+    async def _lookup_3pid_v2(
+        self, id_server: str, id_access_token: str, medium: str, address: str
+    ) -> Optional[str]:
         """Looks up a 3pid in the passed identity server using v2 lookup.
 
         Args:
-            id_server (str): The server name (including port, if required)
+            id_server: The server name (including port, if required)
                 of the identity server to use.
-            id_access_token (str): The access token to authenticate to the identity server with
-            medium (str): The type of the third party identifier (e.g. "email").
-            address (str): The third party identifier (e.g. "foo@example.com").
+            id_access_token: The access token to authenticate to the identity server with
+            medium: The type of the third party identifier (e.g. "email").
+            address: The third party identifier (e.g. "foo@example.com").
 
         Returns:
-            Deferred[str|None]: the matrix ID of the 3pid, or None if it is not recognised.
+            the matrix ID of the 3pid, or None if it is not recognised.
         """
         # Check what hashing details are supported by this identity server
         try:
@@ -757,49 +777,48 @@ class IdentityHandler(BaseHandler):
 
     async def ask_id_server_for_third_party_invite(
         self,
-        requester,
-        id_server,
-        medium,
-        address,
-        room_id,
-        inviter_user_id,
-        room_alias,
-        room_avatar_url,
-        room_join_rules,
-        room_name,
-        inviter_display_name,
-        inviter_avatar_url,
-        id_access_token=None,
-    ):
+        requester: Requester,
+        id_server: str,
+        medium: str,
+        address: str,
+        room_id: str,
+        inviter_user_id: str,
+        room_alias: str,
+        room_avatar_url: str,
+        room_join_rules: str,
+        room_name: str,
+        inviter_display_name: str,
+        inviter_avatar_url: str,
+        id_access_token: Optional[str] = None,
+    ) -> Tuple[str, List[Dict[str, str]], Dict[str, str], str]:
         """
         Asks an identity server for a third party invite.
 
         Args:
-            requester (Requester)
-            id_server (str): hostname + optional port for the identity server.
-            medium (str): The literal string "email".
-            address (str): The third party address being invited.
-            room_id (str): The ID of the room to which the user is invited.
-            inviter_user_id (str): The user ID of the inviter.
-            room_alias (str): An alias for the room, for cosmetic notifications.
-            room_avatar_url (str): The URL of the room's avatar, for cosmetic
+            requester
+            id_server: hostname + optional port for the identity server.
+            medium: The literal string "email".
+            address: The third party address being invited.
+            room_id: The ID of the room to which the user is invited.
+            inviter_user_id: The user ID of the inviter.
+            room_alias: An alias for the room, for cosmetic notifications.
+            room_avatar_url: The URL of the room's avatar, for cosmetic
                 notifications.
-            room_join_rules (str): The join rules of the email (e.g. "public").
-            room_name (str): The m.room.name of the room.
-            inviter_display_name (str): The current display name of the
+            room_join_rules: The join rules of the email (e.g. "public").
+            room_name: The m.room.name of the room.
+            inviter_display_name: The current display name of the
                 inviter.
-            inviter_avatar_url (str): The URL of the inviter's avatar.
+            inviter_avatar_url: The URL of the inviter's avatar.
             id_access_token (str|None): The access token to authenticate to the identity
                 server with
 
         Returns:
-            A deferred tuple containing:
-                token (str): The token which must be signed to prove authenticity.
+            A tuple containing:
+                token: The token which must be signed to prove authenticity.
                 public_keys ([{"public_key": str, "key_validity_url": str}]):
                     public_key is a base64-encoded ed25519 public key.
                 fallback_public_key: One element from public_keys.
-                display_name (str): A user-friendly name to represent the invited
-                    user.
+                display_name: A user-friendly name to represent the invited user.
         """
         invite_config = {
             "medium": medium,
@@ -896,15 +915,15 @@ class IdentityHandler(BaseHandler):
         return token, public_keys, fallback_public_key, display_name
 
 
-def create_id_access_token_header(id_access_token):
+def create_id_access_token_header(id_access_token: str) -> List[str]:
     """Create an Authorization header for passing to SimpleHttpClient as the header value
     of an HTTP request.
 
     Args:
-        id_access_token (str): An identity server access token.
+        id_access_token: An identity server access token.
 
     Returns:
-        list[str]: The ascii-encoded bearer token encased in a list.
+        The ascii-encoded bearer token encased in a list.
     """
     # Prefix with Bearer
     bearer_token = "Bearer %s" % id_access_token
diff --git a/synapse/handlers/room.py b/synapse/handlers/room.py
index fb37d371ad..0c5b99234d 100644
--- a/synapse/handlers/room.py
+++ b/synapse/handlers/room.py
@@ -119,7 +119,7 @@ class RoomCreationHandler(BaseHandler):
 
     async def upgrade_room(
         self, requester: Requester, old_room_id: str, new_version: RoomVersion
-    ):
+    ) -> str:
         """Replace a room with a new room with a different version
 
         Args:
@@ -128,7 +128,7 @@ class RoomCreationHandler(BaseHandler):
             new_version: the new room version to use
 
         Returns:
-            Deferred[unicode]: the new room id
+            the new room id
         """
         await self.ratelimit(requester)
 
@@ -239,7 +239,7 @@ class RoomCreationHandler(BaseHandler):
         old_room_id: str,
         new_room_id: str,
         old_room_state: StateMap[str],
-    ):
+    ) -> None:
         """Send updated power levels in both rooms after an upgrade
 
         Args:
@@ -247,9 +247,6 @@ class RoomCreationHandler(BaseHandler):
             old_room_id: the id of the room to be replaced
             new_room_id: the id of the replacement room
             old_room_state: the state map for the old room
-
-        Returns:
-            Deferred
         """
         old_room_pl_event_id = old_room_state.get((EventTypes.PowerLevels, ""))
 
@@ -322,7 +319,7 @@ class RoomCreationHandler(BaseHandler):
         new_room_id: str,
         new_room_version: RoomVersion,
         tombstone_event_id: str,
-    ):
+    ) -> None:
         """Populate a new room based on an old room
 
         Args:
@@ -332,8 +329,6 @@ class RoomCreationHandler(BaseHandler):
                 created with _gemerate_room_id())
             new_room_version: the new room version to use
             tombstone_event_id: the ID of the tombstone event in the old room.
-        Returns:
-            Deferred
         """
         user_id = requester.user.to_string()
 
diff --git a/synapse/handlers/search.py b/synapse/handlers/search.py
index 4d40d3ac9c..9b312a1558 100644
--- a/synapse/handlers/search.py
+++ b/synapse/handlers/search.py
@@ -15,6 +15,7 @@
 
 import itertools
 import logging
+from typing import Iterable
 
 from unpaddedbase64 import decode_base64, encode_base64
 
@@ -37,7 +38,7 @@ class SearchHandler(BaseHandler):
         self.state_store = self.storage.state
         self.auth = hs.get_auth()
 
-    async def get_old_rooms_from_upgraded_room(self, room_id):
+    async def get_old_rooms_from_upgraded_room(self, room_id: str) -> Iterable[str]:
         """Retrieves room IDs of old rooms in the history of an upgraded room.
 
         We do so by checking the m.room.create event of the room for a
@@ -48,10 +49,10 @@ class SearchHandler(BaseHandler):
         The full list of all found rooms in then returned.
 
         Args:
-            room_id (str): id of the room to search through.
+            room_id: id of the room to search through.
 
         Returns:
-            Deferred[iterable[str]]: predecessor room ids
+            Predecessor room ids
         """
 
         historical_room_ids = []
diff --git a/synapse/handlers/sync.py b/synapse/handlers/sync.py
index 365d7323e4..ebd3e98105 100644
--- a/synapse/handlers/sync.py
+++ b/synapse/handlers/sync.py
@@ -421,10 +421,6 @@ class SyncHandler(object):
         potential_recents: Optional[List[EventBase]] = None,
         newly_joined_room: bool = False,
     ) -> TimelineBatch:
-        """
-        Returns:
-            a Deferred TimelineBatch
-        """
         with Measure(self.clock, "load_filtered_recents"):
             timeline_limit = sync_config.filter_collection.timeline_limit()
             block_all_timeline = (
diff --git a/tox.ini b/tox.ini
index 834d68aea5..595ab3ba66 100644
--- a/tox.ini
+++ b/tox.ini
@@ -185,6 +185,7 @@ commands = mypy \
             synapse/handlers/cas_handler.py \
             synapse/handlers/directory.py \
             synapse/handlers/federation.py \
+            synapse/handlers/identity.py \
             synapse/handlers/oidc_handler.py \
             synapse/handlers/presence.py \
             synapse/handlers/room_member.py \