diff --git a/changelog.d/10446.misc b/changelog.d/10446.misc
new file mode 100644
index 000000000..a5a0ca80e
--- /dev/null
+++ b/changelog.d/10446.misc
@@ -0,0 +1 @@
+Update type annotations to work with forthcoming Twisted 21.7.0 release.
diff --git a/synapse/http/federation/matrix_federation_agent.py b/synapse/http/federation/matrix_federation_agent.py
index 950770201..c16b7f10e 100644
--- a/synapse/http/federation/matrix_federation_agent.py
+++ b/synapse/http/federation/matrix_federation_agent.py
@@ -27,7 +27,7 @@ from twisted.internet.interfaces import (
 )
 from twisted.web.client import URI, Agent, HTTPConnectionPool
 from twisted.web.http_headers import Headers
-from twisted.web.iweb import IAgent, IAgentEndpointFactory, IBodyProducer
+from twisted.web.iweb import IAgent, IAgentEndpointFactory, IBodyProducer, IResponse
 
 from synapse.crypto.context_factory import FederationPolicyForHTTPS
 from synapse.http.client import BlacklistingAgentWrapper
@@ -116,7 +116,7 @@ class MatrixFederationAgent:
         uri: bytes,
         headers: Optional[Headers] = None,
         bodyProducer: Optional[IBodyProducer] = None,
-    ) -> Generator[defer.Deferred, Any, defer.Deferred]:
+    ) -> Generator[defer.Deferred, Any, IResponse]:
         """
         Args:
             method: HTTP method: GET/POST/etc
diff --git a/synapse/logging/context.py b/synapse/logging/context.py
index 18ac50780..02e5ddd2e 100644
--- a/synapse/logging/context.py
+++ b/synapse/logging/context.py
@@ -25,7 +25,7 @@ See doc/log_contexts.rst for details on how this works.
 import inspect
 import logging
 import threading
-import types
+import typing
 import warnings
 from typing import TYPE_CHECKING, Optional, Tuple, TypeVar, Union
 
@@ -745,7 +745,7 @@ def run_in_background(f, *args, **kwargs) -> defer.Deferred:
         # by synchronous exceptions, so let's turn them into Failures.
         return defer.fail()
 
-    if isinstance(res, types.CoroutineType):
+    if isinstance(res, typing.Coroutine):
         res = defer.ensureDeferred(res)
 
     # At this point we should have a Deferred, if not then f was a synchronous
diff --git a/synapse/module_api/__init__.py b/synapse/module_api/__init__.py
index 1259fc2d9..473812b8e 100644
--- a/synapse/module_api/__init__.py
+++ b/synapse/module_api/__init__.py
@@ -484,7 +484,7 @@ class ModuleApi:
     @defer.inlineCallbacks
     def get_state_events_in_room(
         self, room_id: str, types: Iterable[Tuple[str, Optional[str]]]
-    ) -> Generator[defer.Deferred, Any, defer.Deferred]:
+    ) -> Generator[defer.Deferred, Any, Iterable[EventBase]]:
         """Gets current state events for the given room.
 
         (This is exposed for compatibility with the old SpamCheckerApi. We should