diff --git a/changelog.d/16235.misc b/changelog.d/16235.misc
new file mode 100644
index 000000000..b1533f93b
--- /dev/null
+++ b/changelog.d/16235.misc
@@ -0,0 +1 @@
+Fix type checking when using the new version of Twisted.
diff --git a/poetry.lock b/poetry.lock
index 1cefabb35..872a863ed 100644
--- a/poetry.lock
+++ b/poetry.lock
@@ -2866,44 +2866,43 @@ urllib3 = ">=1.26.0"
 
 [[package]]
 name = "twisted"
-version = "22.10.0"
+version = "23.8.0"
 description = "An asynchronous networking framework written in Python"
 optional = false
 python-versions = ">=3.7.1"
 files = [
-    {file = "Twisted-22.10.0-py3-none-any.whl", hash = "sha256:86c55f712cc5ab6f6d64e02503352464f0400f66d4f079096d744080afcccbd0"},
-    {file = "Twisted-22.10.0.tar.gz", hash = "sha256:32acbd40a94f5f46e7b42c109bfae2b302250945561783a8b7a059048f2d4d31"},
+    {file = "twisted-23.8.0-py3-none-any.whl", hash = "sha256:b8bdba145de120ffb36c20e6e071cce984e89fba798611ed0704216fb7f884cd"},
+    {file = "twisted-23.8.0.tar.gz", hash = "sha256:3c73360add17336a622c0d811c2a2ce29866b6e59b1125fd6509b17252098a24"},
 ]
 
 [package.dependencies]
-attrs = ">=19.2.0"
-Automat = ">=0.8.0"
+attrs = ">=21.3.0"
+automat = ">=0.8.0"
 constantly = ">=15.1"
 hyperlink = ">=17.1.1"
 idna = {version = ">=2.4", optional = true, markers = "extra == \"tls\""}
-incremental = ">=21.3.0"
+incremental = ">=22.10.0"
 pyopenssl = {version = ">=21.0.0", optional = true, markers = "extra == \"tls\""}
 service-identity = {version = ">=18.1.0", optional = true, markers = "extra == \"tls\""}
 twisted-iocpsupport = {version = ">=1.0.2,<2", markers = "platform_system == \"Windows\""}
-typing-extensions = ">=3.6.5"
-"zope.interface" = ">=4.4.2"
+typing-extensions = ">=3.10.0"
+zope-interface = ">=5"
 
 [package.extras]
-all-non-platform = ["PyHamcrest (>=1.9.0)", "appdirs (>=1.4.0)", "bcrypt (>=3.0.0)", "contextvars (>=2.4,<3)", "cryptography (>=2.6)", "cython-test-exception-raiser (>=1.0.2,<2)", "h2 (>=3.0,<5.0)", "hypothesis (>=6.0,<7.0)", "idna (>=2.4)", "priority (>=1.1.0,<2.0)", "pyasn1", "pyopenssl (>=21.0.0)", "pyserial (>=3.0)", "pywin32 (!=226)", "service-identity (>=18.1.0)"]
-conch = ["appdirs (>=1.4.0)", "bcrypt (>=3.0.0)", "cryptography (>=2.6)", "pyasn1"]
-conch-nacl = ["PyNaCl", "appdirs (>=1.4.0)", "bcrypt (>=3.0.0)", "cryptography (>=2.6)", "pyasn1"]
+all-non-platform = ["twisted[conch,contextvars,http2,serial,test,tls]", "twisted[conch,contextvars,http2,serial,test,tls]"]
+conch = ["appdirs (>=1.4.0)", "bcrypt (>=3.1.3)", "cryptography (>=3.3)"]
 contextvars = ["contextvars (>=2.4,<3)"]
-dev = ["coverage (>=6b1,<7)", "pydoctor (>=22.9.0,<22.10.0)", "pyflakes (>=2.2,<3.0)", "python-subunit (>=1.4,<2.0)", "readthedocs-sphinx-ext (>=2.1,<3.0)", "sphinx (>=5.0,<6)", "sphinx-rtd-theme (>=1.0,<2.0)", "towncrier (>=22.8,<23.0)", "twistedchecker (>=0.7,<1.0)"]
-dev-release = ["pydoctor (>=22.9.0,<22.10.0)", "readthedocs-sphinx-ext (>=2.1,<3.0)", "sphinx (>=5.0,<6)", "sphinx-rtd-theme (>=1.0,<2.0)", "towncrier (>=22.8,<23.0)"]
-gtk-platform = ["PyHamcrest (>=1.9.0)", "appdirs (>=1.4.0)", "bcrypt (>=3.0.0)", "contextvars (>=2.4,<3)", "cryptography (>=2.6)", "cython-test-exception-raiser (>=1.0.2,<2)", "h2 (>=3.0,<5.0)", "hypothesis (>=6.0,<7.0)", "idna (>=2.4)", "priority (>=1.1.0,<2.0)", "pyasn1", "pygobject", "pyopenssl (>=21.0.0)", "pyserial (>=3.0)", "pywin32 (!=226)", "service-identity (>=18.1.0)"]
+dev = ["coverage (>=6b1,<7)", "pyflakes (>=2.2,<3.0)", "python-subunit (>=1.4,<2.0)", "twisted[dev-release]", "twistedchecker (>=0.7,<1.0)"]
+dev-release = ["pydoctor (>=23.4.0,<23.5.0)", "pydoctor (>=23.4.0,<23.5.0)", "readthedocs-sphinx-ext (>=2.2,<3.0)", "readthedocs-sphinx-ext (>=2.2,<3.0)", "sphinx (>=5,<7)", "sphinx (>=5,<7)", "sphinx-rtd-theme (>=1.2,<2.0)", "sphinx-rtd-theme (>=1.2,<2.0)", "towncrier (>=22.12,<23.0)", "towncrier (>=22.12,<23.0)", "urllib3 (<2)", "urllib3 (<2)"]
+gtk-platform = ["pygobject", "pygobject", "twisted[all-non-platform]", "twisted[all-non-platform]"]
 http2 = ["h2 (>=3.0,<5.0)", "priority (>=1.1.0,<2.0)"]
-macos-platform = ["PyHamcrest (>=1.9.0)", "appdirs (>=1.4.0)", "bcrypt (>=3.0.0)", "contextvars (>=2.4,<3)", "cryptography (>=2.6)", "cython-test-exception-raiser (>=1.0.2,<2)", "h2 (>=3.0,<5.0)", "hypothesis (>=6.0,<7.0)", "idna (>=2.4)", "priority (>=1.1.0,<2.0)", "pyasn1", "pyobjc-core", "pyobjc-framework-CFNetwork", "pyobjc-framework-Cocoa", "pyopenssl (>=21.0.0)", "pyserial (>=3.0)", "pywin32 (!=226)", "service-identity (>=18.1.0)"]
-mypy = ["PyHamcrest (>=1.9.0)", "PyNaCl", "appdirs (>=1.4.0)", "bcrypt (>=3.0.0)", "contextvars (>=2.4,<3)", "coverage (>=6b1,<7)", "cryptography (>=2.6)", "cython-test-exception-raiser (>=1.0.2,<2)", "h2 (>=3.0,<5.0)", "hypothesis (>=6.0,<7.0)", "idna (>=2.4)", "mypy (==0.930)", "mypy-zope (==0.3.4)", "priority (>=1.1.0,<2.0)", "pyasn1", "pydoctor (>=22.9.0,<22.10.0)", "pyflakes (>=2.2,<3.0)", "pyopenssl (>=21.0.0)", "pyserial (>=3.0)", "python-subunit (>=1.4,<2.0)", "pywin32 (!=226)", "readthedocs-sphinx-ext (>=2.1,<3.0)", "service-identity (>=18.1.0)", "sphinx (>=5.0,<6)", "sphinx-rtd-theme (>=1.0,<2.0)", "towncrier (>=22.8,<23.0)", "twistedchecker (>=0.7,<1.0)", "types-pyOpenSSL", "types-setuptools"]
-osx-platform = ["PyHamcrest (>=1.9.0)", "appdirs (>=1.4.0)", "bcrypt (>=3.0.0)", "contextvars (>=2.4,<3)", "cryptography (>=2.6)", "cython-test-exception-raiser (>=1.0.2,<2)", "h2 (>=3.0,<5.0)", "hypothesis (>=6.0,<7.0)", "idna (>=2.4)", "priority (>=1.1.0,<2.0)", "pyasn1", "pyobjc-core", "pyobjc-framework-CFNetwork", "pyobjc-framework-Cocoa", "pyopenssl (>=21.0.0)", "pyserial (>=3.0)", "pywin32 (!=226)", "service-identity (>=18.1.0)"]
+macos-platform = ["pyobjc-core", "pyobjc-core", "pyobjc-framework-cfnetwork", "pyobjc-framework-cfnetwork", "pyobjc-framework-cocoa", "pyobjc-framework-cocoa", "twisted[all-non-platform]", "twisted[all-non-platform]"]
+mypy = ["mypy (==0.981)", "mypy-extensions (==0.4.3)", "mypy-zope (==0.3.11)", "twisted[all-non-platform,dev]", "types-pyopenssl", "types-setuptools"]
+osx-platform = ["twisted[macos-platform]", "twisted[macos-platform]"]
 serial = ["pyserial (>=3.0)", "pywin32 (!=226)"]
-test = ["PyHamcrest (>=1.9.0)", "cython-test-exception-raiser (>=1.0.2,<2)", "hypothesis (>=6.0,<7.0)"]
+test = ["cython-test-exception-raiser (>=1.0.2,<2)", "hypothesis (>=6.56)", "pyhamcrest (>=2)"]
 tls = ["idna (>=2.4)", "pyopenssl (>=21.0.0)", "service-identity (>=18.1.0)"]
-windows-platform = ["PyHamcrest (>=1.9.0)", "appdirs (>=1.4.0)", "bcrypt (>=3.0.0)", "contextvars (>=2.4,<3)", "cryptography (>=2.6)", "cython-test-exception-raiser (>=1.0.2,<2)", "h2 (>=3.0,<5.0)", "hypothesis (>=6.0,<7.0)", "idna (>=2.4)", "priority (>=1.1.0,<2.0)", "pyasn1", "pyopenssl (>=21.0.0)", "pyserial (>=3.0)", "pywin32 (!=226)", "pywin32 (!=226)", "service-identity (>=18.1.0)"]
+windows-platform = ["pywin32 (!=226)", "pywin32 (!=226)", "twisted[all-non-platform]", "twisted[all-non-platform]"]
 
 [[package]]
 name = "twisted-iocpsupport"
diff --git a/synapse/handlers/initial_sync.py b/synapse/handlers/initial_sync.py
index b3be7a86f..5dc76ef58 100644
--- a/synapse/handlers/initial_sync.py
+++ b/synapse/handlers/initial_sync.py
@@ -13,7 +13,7 @@
 # limitations under the License.
 
 import logging
-from typing import TYPE_CHECKING, List, Optional, Tuple, cast
+from typing import TYPE_CHECKING, List, Optional, Tuple
 
 from synapse.api.constants import (
     AccountDataTypes,
@@ -23,7 +23,6 @@ from synapse.api.constants import (
     Membership,
 )
 from synapse.api.errors import SynapseError
-from synapse.events import EventBase
 from synapse.events.utils import SerializeEventConfig
 from synapse.events.validator import EventValidator
 from synapse.handlers.presence import format_user_presence_state
@@ -35,7 +34,6 @@ from synapse.types import (
     JsonDict,
     Requester,
     RoomStreamToken,
-    StateMap,
     StreamKeyType,
     StreamToken,
     UserID,
@@ -199,9 +197,7 @@ class InitialSyncHandler:
                     deferred_room_state = run_in_background(
                         self._state_storage_controller.get_state_for_events,
                         [event.event_id],
-                    ).addCallback(
-                        lambda states: cast(StateMap[EventBase], states[event.event_id])
-                    )
+                    ).addCallback(lambda states: states[event.event_id])
 
                 (messages, token), current_state = await make_deferred_yieldable(
                     gather_results(
diff --git a/synapse/logging/context.py b/synapse/logging/context.py
index 64c6ae451..bf7e31102 100644
--- a/synapse/logging/context.py
+++ b/synapse/logging/context.py
@@ -728,7 +728,7 @@ async def _unwrap_awaitable(awaitable: Awaitable[R]) -> R:
 
 
 @overload
-def preserve_fn(  # type: ignore[misc]
+def preserve_fn(
     f: Callable[P, Awaitable[R]],
 ) -> Callable[P, "defer.Deferred[R]"]:
     # The `type: ignore[misc]` above suppresses
@@ -756,7 +756,7 @@ def preserve_fn(
 
 
 @overload
-def run_in_background(  # type: ignore[misc]
+def run_in_background(
     f: Callable[P, Awaitable[R]], *args: P.args, **kwargs: P.kwargs
 ) -> "defer.Deferred[R]":
     # The `type: ignore[misc]` above suppresses
diff --git a/synapse/util/gai_resolver.py b/synapse/util/gai_resolver.py
index 214eb17fb..fecf829ad 100644
--- a/synapse/util/gai_resolver.py
+++ b/synapse/util/gai_resolver.py
@@ -136,7 +136,7 @@ class GAIResolver:
 
     # The types on IHostnameResolver is incorrect in Twisted, see
     # https://twistedmatrix.com/trac/ticket/10276
-    def resolveHostName(  # type: ignore[override]
+    def resolveHostName(
         self,
         resolutionReceiver: IResolutionReceiver,
         hostName: str,