diff --git a/.github/workflows/tests.yml b/.github/workflows/tests.yml
index 320caa8..d8b7d4d 100644
--- a/.github/workflows/tests.yml
+++ b/.github/workflows/tests.yml
@@ -81,17 +81,21 @@ jobs:
     runs-on: ${{ matrix.os }}
     strategy:
       matrix:
-        python-version: [pypy-3.9, 3.7, 3.8, 3.9, '3.10', '3.11', "3.12-dev"]
+        python-version: [pypy-3.10, 3.8, 3.9, '3.10', '3.11', "3.12", "3.13.0-beta.1"]
         os: [ubuntu-latest, macos-latest]
         exclude:
           - os: macos-latest
-            python-version: pypy-3.9
+            python-version: pypy-3.10
+          - os: macos-latest
+            python-version: "3.8"
+          - os: macos-latest
+            python-version: "3.9"
     steps:
       - name: checkout
-        uses: actions/checkout@v3
+        uses: actions/checkout@v4
 
       - name: Set up Python ${{ matrix.python-version }}
-        uses: actions/setup-python@v4
+        uses: actions/setup-python@v5
         with:
           python-version: ${{ matrix.python-version }}
           cache: 'pip'
@@ -100,14 +104,13 @@ jobs:
       - name: Install Build Dependencies
         run: |
           pip install -U pip
-          pip install -U setuptools wheel twine
-          pip install -U 'cython>=3.0b3'
+          pip install -U setuptools wheel twine build
+          pip install -U 'cython>=3.0.10'
           pip install -U coverage
-
       - name: Install perfmetrics (non-Mac)
         if: ${{ ! startsWith(runner.os, 'Mac') }}
         run: |
-          python setup.py bdist_wheel
+          python -m build
           python -m pip install -U -e ".[test,docs]"
         env:
           # Ensure we test with assertions enabled.
@@ -120,7 +123,7 @@ jobs:
       - name: Install perfmetrics (Mac)
         if: startsWith(runner.os, 'Mac')
         run: |
-          python setup.py bdist_wheel
+          python -m build
           python -m pip install -U -e ".[test,docs]"
         env:
           # Unlike the above, we are actually distributing these
@@ -135,7 +138,7 @@ jobs:
           twine check dist/*
 
       - name: Upload perfmetrics wheel
-        uses: actions/upload-artifact@v2
+        uses: actions/upload-artifact@v3
         with:
           name: perfmetrics-${{ runner.os }}-${{ matrix.python-version }}.whl
           path: dist/*whl
@@ -169,9 +172,8 @@ jobs:
     # We use a regular Python matrix entry to share as much code as possible.
     strategy:
       matrix:
-        python-version: [3.9]
+        python-version: [3.11]
         image:
-          - manylinux2010_x86_64
           - manylinux2014_aarch64
           - manylinux2014_ppc64le
           - manylinux2014_s390x
@@ -181,9 +183,9 @@ jobs:
     name: ${{ matrix.image }}
     steps:
       - name: checkout
-        uses: actions/checkout@v3
+        uses: actions/checkout@v4
       - name: Set up Python ${{ matrix.python-version }}
-        uses: actions/setup-python@v4
+        uses: actions/setup-python@v5
         with:
           python-version: ${{ matrix.python-version }}
       - name: Set up QEMU
diff --git a/CHANGES.rst b/CHANGES.rst
index a9b303f..fd6182a 100644
--- a/CHANGES.rst
+++ b/CHANGES.rst
@@ -2,11 +2,12 @@
  CHANGES
 =========
 
-4.0.1 (unreleased)
+4.1.0 (unreleased)
 ==================
 
-- Nothing changed yet.
-
+- Add support for Python 3.13.
+- Drop support for Python 3.7.
+- Drop support for Manylinux 2010 wheels.
 
 4.0.0 (2023-06-22)
 ==================
diff --git a/pyproject.toml b/pyproject.toml
index 7c7b2c5..8835d22 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -19,5 +19,5 @@ requires = [
      # failing in Python 2 (https://travis-ci.org/github/gevent/gevent/jobs/683782800);
      # This was fixed in 3.0a5 (https://github.com/cython/cython/issues/3578)
      # 3.0a6 fixes an issue cythonizing source on 32-bit platforms
-     "Cython >= 3.0b3; platform_python_implementation == 'CPython'",
+     "Cython >= 3.0.10; platform_python_implementation == 'CPython'",
 ]
diff --git a/scripts/releases/make-manylinux b/scripts/releases/make-manylinux
index 2c57643..40e7138 100755
--- a/scripts/releases/make-manylinux
+++ b/scripts/releases/make-manylinux
@@ -17,21 +17,25 @@ export CXXFLAGS="-pipe -O3 -DNDEBUG"
 
 if [ -d /io -a -d /opt/python ]; then
     # Running inside docker
+    # 2024-06-11: git started complaining "fatal: detected dubious ownership in repository at '/io/.git'"
+    git config --global --add safe.directory /io/.git
     cd /io
     rm -rf wheelhouse
     mkdir wheelhouse
-    for variant in `ls -d /opt/python/cp{37,38,39,310,311,312}*`; do
+    # non-gil won't build, seems like a cython issue.
+    rm -f /opt/python/cp313-cp313t
+    for variant in `ls -d /opt/python/cp{38,39,310,311,312,313}*`; do
         echo "Building $variant"
         mkdir /tmp/build
         cd /tmp/build
         git clone /io io
         cd io
         $variant/bin/pip install -U pip
-        $variant/bin/pip install -U 'cython>=3.0b3' setuptools
-        PATH=$variant/bin:$PATH $variant/bin/python setup.py bdist_wheel
-        auditwheel show dist/*.whl
-        auditwheel repair dist/*.whl
-        cp wheelhouse/*.whl /io/wheelhouse
+        $variant/bin/pip install -U 'cython>=3.0.10' setuptools build wheel
+        PATH=$variant/bin:$PATH $variant/bin/python -m build --wheel
+        auditwheel show dist/perfmetrics*.whl
+        auditwheel repair dist/perfmetrics*.whl
+        cp wheelhouse/perfmetrics*.whl /io/wheelhouse
         cd /io
         rm -rf /tmp/build
     done
diff --git a/setup.py b/setup.py
index a85b245..f611f0d 100644
--- a/setup.py
+++ b/setup.py
@@ -18,9 +18,9 @@ def read(fname, here=os.path.dirname(__file__)):
 tests_require = [
     'zope.testrunner',
     # nti.testing > ZODB > persistent -> cffi
-    # But cffi won't build on apple silicon on 3.12.
-    # Can't get persistent to build on PyPy 3.9 either.
-    'nti.testing; (python_version != "3.12" and platform_machine != "arm64" and platform_system != "Darwin") and platform_python_implementation != "PyPy"',
+    # CffI won't build on 3.13 yet; persistent is having trouble on PyPy
+    'nti.testing; python_version != "3.13" and platform_python_implementation != "PyPy"',
+
     # transitive dep of nti.testing, which we don't always have, but need
     # for our emulation
     'zope.schema',
@@ -125,7 +125,7 @@ def _c(m):
 
 setup(
     name='perfmetrics',
-    version='4.0.1.dev0',
+    version='4.1.0.dev0',
     author='Shane Hathaway',
     author_email='shane@hathawaymix.org',
     maintainer='Jason Madden',
@@ -140,12 +140,12 @@ def _c(m):
         "Intended Audience :: Developers",
         "Programming Language :: Python :: 3",
         "Programming Language :: Python :: 3 :: Only",
-        "Programming Language :: Python :: 3.7",
         "Programming Language :: Python :: 3.8",
         "Programming Language :: Python :: 3.9",
         "Programming Language :: Python :: 3.10",
         "Programming Language :: Python :: 3.11",
         "Programming Language :: Python :: 3.12",
+        "Programming Language :: Python :: 3.13",
         "Programming Language :: Python :: Implementation :: CPython",
         "Programming Language :: Python :: Implementation :: PyPy",
         "License :: Repoze Public License",
diff --git a/tox.ini b/tox.ini
index 6cb3c8b..e53aaad 100644
--- a/tox.ini
+++ b/tox.ini
@@ -1,5 +1,5 @@
 [tox]
-envlist = py37,py38,py39,py310,py311,py312,pypy3,py37,coverage
+envlist = py37,py38,py39,py310,py311,py312,py313,pypy3,py37,coverage
 
 [testenv]
 extras =