diff --git a/changelog.d/9031.misc b/changelog.d/9031.misc
new file mode 100644
index 0000000000..f43611c385
--- /dev/null
+++ b/changelog.d/9031.misc
@@ -0,0 +1 @@
+Fix running unit tests when optional dependencies are not installed.
diff --git a/tests/handlers/test_oidc.py b/tests/handlers/test_oidc.py
index 368d600b33..f5df657814 100644
--- a/tests/handlers/test_oidc.py
+++ b/tests/handlers/test_oidc.py
@@ -24,7 +24,6 @@ import pymacaroons
 from twisted.web.resource import Resource
 
 from synapse.api.errors import RedirectException
-from synapse.handlers.oidc_handler import OidcError
 from synapse.handlers.sso import MappingException
 from synapse.rest.client.v1 import login
 from synapse.rest.synapse.client.pick_username import pick_username_resource
@@ -34,6 +33,14 @@ from synapse.types import UserID
 from tests.test_utils import FakeResponse, simple_async_mock
 from tests.unittest import HomeserverTestCase, override_config
 
+try:
+    import authlib  # noqa: F401
+
+    HAS_OIDC = True
+except ImportError:
+    HAS_OIDC = False
+
+
 # These are a few constants that are used as config parameters in the tests.
 ISSUER = "https://issuer/"
 CLIENT_ID = "test-client-id"
@@ -113,6 +120,9 @@ async def get_json(url):
 
 
 class OidcHandlerTestCase(HomeserverTestCase):
+    if not HAS_OIDC:
+        skip = "requires OIDC"
+
     def default_config(self):
         config = super().default_config()
         config["public_baseurl"] = BASE_URL
@@ -458,6 +468,8 @@ class OidcHandlerTestCase(HomeserverTestCase):
         self.assertRenderedError("fetch_error")
 
         # Handle code exchange failure
+        from synapse.handlers.oidc_handler import OidcError
+
         self.handler._exchange_code = simple_async_mock(
             raises=OidcError("invalid_request")
         )
@@ -538,6 +550,8 @@ class OidcHandlerTestCase(HomeserverTestCase):
                 body=b'{"error": "foo", "error_description": "bar"}',
             )
         )
+        from synapse.handlers.oidc_handler import OidcError
+
         exc = self.get_failure(self.handler._exchange_code(code), OidcError)
         self.assertEqual(exc.value.error, "foo")
         self.assertEqual(exc.value.error_description, "bar")
@@ -829,6 +843,9 @@ class OidcHandlerTestCase(HomeserverTestCase):
 
 
 class UsernamePickerTestCase(HomeserverTestCase):
+    if not HAS_OIDC:
+        skip = "requires OIDC"
+
     servlets = [login.register_servlets]
 
     def default_config(self):
diff --git a/tests/rest/client/v1/test_login.py b/tests/rest/client/v1/test_login.py
index 999d628315..901c72d36a 100644
--- a/tests/rest/client/v1/test_login.py
+++ b/tests/rest/client/v1/test_login.py
@@ -4,7 +4,10 @@ import urllib.parse
 
 from mock import Mock
 
-import jwt
+try:
+    import jwt
+except ImportError:
+    jwt = None
 
 import synapse.rest.admin
 from synapse.appservice import ApplicationService
@@ -460,6 +463,9 @@ class CASTestCase(unittest.HomeserverTestCase):
 
 
 class JWTTestCase(unittest.HomeserverTestCase):
+    if not jwt:
+        skip = "requires jwt"
+
     servlets = [
         synapse.rest.admin.register_servlets_for_client_rest_resource,
         login.register_servlets,
@@ -628,6 +634,9 @@ class JWTTestCase(unittest.HomeserverTestCase):
 # RSS256, with a public key configured in synapse as "jwt_secret", and tokens
 # signed by the private key.
 class JWTPubKeyTestCase(unittest.HomeserverTestCase):
+    if not jwt:
+        skip = "requires jwt"
+
     servlets = [
         login.register_servlets,
     ]
diff --git a/tests/rest/client/v2_alpha/test_auth.py b/tests/rest/client/v2_alpha/test_auth.py
index ac66a4e0b7..bb91e0c331 100644
--- a/tests/rest/client/v2_alpha/test_auth.py
+++ b/tests/rest/client/v2_alpha/test_auth.py
@@ -26,8 +26,10 @@ from synapse.rest.oidc import OIDCResource
 from synapse.types import JsonDict, UserID
 
 from tests import unittest
+from tests.handlers.test_oidc import HAS_OIDC
 from tests.rest.client.v1.utils import TEST_OIDC_CONFIG
 from tests.server import FakeChannel
+from tests.unittest import override_config, skip_unless
 
 
 class DummyRecaptchaChecker(UserInteractiveAuthChecker):
@@ -158,20 +160,22 @@ class UIAuthTests(unittest.HomeserverTestCase):
 
     def default_config(self):
         config = super().default_config()
-
-        # we enable OIDC as a way of testing SSO flows
-        oidc_config = {}
-        oidc_config.update(TEST_OIDC_CONFIG)
-        oidc_config["allow_existing_users"] = True
-
-        config["oidc_config"] = oidc_config
         config["public_baseurl"] = "https://synapse.test"
+
+        if HAS_OIDC:
+            # we enable OIDC as a way of testing SSO flows
+            oidc_config = {}
+            oidc_config.update(TEST_OIDC_CONFIG)
+            oidc_config["allow_existing_users"] = True
+            config["oidc_config"] = oidc_config
+
         return config
 
     def create_resource_dict(self):
         resource_dict = super().create_resource_dict()
-        # mount the OIDC resource at /_synapse/oidc
-        resource_dict["/_synapse/oidc"] = OIDCResource(self.hs)
+        if HAS_OIDC:
+            # mount the OIDC resource at /_synapse/oidc
+            resource_dict["/_synapse/oidc"] = OIDCResource(self.hs)
         return resource_dict
 
     def prepare(self, reactor, clock, hs):
@@ -380,6 +384,8 @@ class UIAuthTests(unittest.HomeserverTestCase):
         # Note that *no auth* information is provided, not even a session iD!
         self.delete_device(self.user_tok, self.device_id, 200)
 
+    @skip_unless(HAS_OIDC, "requires OIDC")
+    @override_config({"oidc_config": TEST_OIDC_CONFIG})
     def test_does_not_offer_password_for_sso_user(self):
         login_resp = self.helper.login_via_oidc("username")
         user_tok = login_resp["access_token"]
@@ -393,13 +399,13 @@ class UIAuthTests(unittest.HomeserverTestCase):
         self.assertEqual(flows, [{"stages": ["m.login.sso"]}])
 
     def test_does_not_offer_sso_for_password_user(self):
-        # now call the device deletion API: we should get the option to auth with SSO
-        # and not password.
         channel = self.delete_device(self.user_tok, self.device_id, 401)
 
         flows = channel.json_body["flows"]
         self.assertEqual(flows, [{"stages": ["m.login.password"]}])
 
+    @skip_unless(HAS_OIDC, "requires OIDC")
+    @override_config({"oidc_config": TEST_OIDC_CONFIG})
     def test_offers_both_flows_for_upgraded_user(self):
         """A user that had a password and then logged in with SSO should get both flows
         """
diff --git a/tests/rest/media/v1/test_url_preview.py b/tests/rest/media/v1/test_url_preview.py
index 83d728b4a4..6968502433 100644
--- a/tests/rest/media/v1/test_url_preview.py
+++ b/tests/rest/media/v1/test_url_preview.py
@@ -26,8 +26,15 @@ from twisted.test.proto_helpers import AccumulatingProtocol
 from tests import unittest
 from tests.server import FakeTransport
 
+try:
+    import lxml
+except ImportError:
+    lxml = None
+
 
 class URLPreviewTests(unittest.HomeserverTestCase):
+    if not lxml:
+        skip = "url preview feature requires lxml"
 
     hijack_auth = True
     user_id = "@test:user"
diff --git a/tests/test_preview.py b/tests/test_preview.py
index a883d707df..c19facc1cb 100644
--- a/tests/test_preview.py
+++ b/tests/test_preview.py
@@ -20,8 +20,16 @@ from synapse.rest.media.v1.preview_url_resource import (
 
 from . import unittest
 
+try:
+    import lxml
+except ImportError:
+    lxml = None
+
 
 class PreviewTestCase(unittest.TestCase):
+    if not lxml:
+        skip = "url preview feature requires lxml"
+
     def test_long_summarize(self):
         example_paras = [
             """Tromsø (Norwegian pronunciation: [ˈtrʊmsœ] ( listen); Northern Sami:
@@ -137,6 +145,9 @@ class PreviewTestCase(unittest.TestCase):
 
 
 class PreviewUrlTestCase(unittest.TestCase):
+    if not lxml:
+        skip = "url preview feature requires lxml"
+
     def test_simple(self):
         html = """
         <html>
diff --git a/tests/unittest.py b/tests/unittest.py
index af7f752c5a..bbd295687c 100644
--- a/tests/unittest.py
+++ b/tests/unittest.py
@@ -20,7 +20,7 @@ import hmac
 import inspect
 import logging
 import time
-from typing import Dict, Iterable, Optional, Tuple, Type, TypeVar, Union
+from typing import Callable, Dict, Iterable, Optional, Tuple, Type, TypeVar, Union
 
 from mock import Mock, patch
 
@@ -736,3 +736,29 @@ def override_config(extra_config):
         return func
 
     return decorator
+
+
+TV = TypeVar("TV")
+
+
+def skip_unless(condition: bool, reason: str) -> Callable[[TV], TV]:
+    """A test decorator which will skip the decorated test unless a condition is set
+
+    For example:
+
+    class MyTestCase(TestCase):
+        @skip_unless(HAS_FOO, "Cannot test without foo")
+        def test_foo(self):
+            ...
+
+    Args:
+        condition: If true, the test will be skipped
+        reason: the reason to give for skipping the test
+    """
+
+    def decorator(f: TV) -> TV:
+        if not condition:
+            f.skip = reason  # type: ignore
+        return f
+
+    return decorator