diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml
index 15cfcbaa64..562495a4a2 100644
--- a/.github/workflows/ci.yml
+++ b/.github/workflows/ci.yml
@@ -181,11 +181,14 @@ jobs:
           #  lsp: 'http://download.pctools.com/mirror/updates/9.0.0.2308-SDavfree-lite_en.exe'
           #  lsp_extract_file: ''
           #  extra_name: ', with non-IFS LSP'
+
+    # ***REMEMBER*** to remove the 3.14 line once windows+cffi works again
     continue-on-error: >-
       ${{
         (
           endsWith(matrix.python, '-dev')
           || endsWith(matrix.python, '-nightly')
+          || matrix.python == '3.14'
         )
         && true
         || false
@@ -387,11 +390,13 @@ jobs:
           - python: '3.9'  # We support running on cython 2 and 3 for 3.9
             cython: '<3'   # cython 2
           - python: '3.9'
-            cython: '>=3'  # cython 3 (or greater)
+    # cython 3.1.0 broke stuff https://github.com/cython/cython/issues/6865
+            cython: '>=3,<3.1'  # cython 3 (or greater)
           - python: '3.11' # 3.11 is the last version Cy2 supports
             cython: '<3'   # cython 2
           - python: '3.13' # We support running cython3 on 3.13
-            cython: '>=3'  # cython 3 (or greater)
+    # cython 3.1.0 broke stuff https://github.com/cython/cython/issues/6865
+            cython: '>=3,<3.1'  # cython 3 (or greater)
     steps:
       - name: Retrieve the project source from an sdist inside the GHA artifact
         uses: re-actors/checkout-python-sdist@release/v2
diff --git a/src/trio/_core/_tests/test_run.py b/src/trio/_core/_tests/test_run.py
index c02d185d45..f3e53ace38 100644
--- a/src/trio/_core/_tests/test_run.py
+++ b/src/trio/_core/_tests/test_run.py
@@ -922,7 +922,13 @@ async def main() -> None:
     gc_collect_harder()
 
 
+# This segfaults, so we need to skipif. Remember to remove the skipif once
+# the upstream issue is resolved.
 @restore_unraisablehook()
+@pytest.mark.skipif(
+    sys.version_info[:3] == (3, 14, 0),
+    reason="https://github.com/python/cpython/issues/133932",
+)
 def test_error_in_run_loop() -> None:
     # Blow stuff up real good to check we at least get a TrioInternalError
     async def main() -> None:
diff --git a/src/trio/_tests/test_exports.py b/src/trio/_tests/test_exports.py
index 0bf619e3b8..1af78513d7 100644
--- a/src/trio/_tests/test_exports.py
+++ b/src/trio/_tests/test_exports.py
@@ -117,6 +117,11 @@ def iter_modules(
 # won't be reflected in trio.socket, and this shouldn't cause downstream test
 # runs to start failing.
 @pytest.mark.redistributors_should_skip
+@pytest.mark.skipif(
+    sys.version_info[:4] == (3, 14, 0, "beta"),
+    # 12 pass, 16 fail
+    reason="several tools don't support 3.14",
+)
 # Static analysis tools often have trouble with alpha releases, where Python's
 # internals are in flux, grammar may not have settled down, etc.
 @pytest.mark.skipif(
@@ -243,6 +248,11 @@ def no_underscores(symbols: Iterable[str]) -> set[str]:
 @slow
 # see comment on test_static_tool_sees_all_symbols
 @pytest.mark.redistributors_should_skip
+@pytest.mark.skipif(
+    sys.version_info[:4] == (3, 14, 0, "beta"),
+    # 2 passes, 12 fails
+    reason="several tools don't support 3.14.0",
+)
 # Static analysis tools often have trouble with alpha releases, where Python's
 # internals are in flux, grammar may not have settled down, etc.
 @pytest.mark.skipif(
diff --git a/tox.ini b/tox.ini
index 6eecf7b78a..39d4dece5d 100644
--- a/tox.ini
+++ b/tox.ini
@@ -52,7 +52,8 @@ commands =
 [testenv:py39-cython2,py39-cython,py311-cython2,py313-cython]
 description = "Run cython tests."
 deps =
-    cython
+    # cython 3.1.0 broke stuff https://github.com/cython/cython/issues/6865
+    cython: cython<3.1.0
     cython2: cython<3
     setuptools ; python_version >= '3.12'
 commands_pre =