diff --git a/.cirrus.yml b/.cirrus.yml
index 189079bc..3970103e 100644
--- a/.cirrus.yml
+++ b/.cirrus.yml
@@ -9,14 +9,12 @@ cirrus_wheels_macos_arm64_task:
   env:
     PATH: /opt/homebrew/opt/python@3.10/bin:$PATH
     CIBW_ARCHS_MACOS: arm64
+    CIBW_TEST_COMMAND: "python -m flint.test"
   install_pre_requirements_script:
-    - brew install python@3.10
-    - ln -s python3 /opt/homebrew/opt/python@3.10/bin/python
-    - which python
-    - python --version
-  install_cibuildwheel_script:
-    - python -m pip install cibuildwheel==2.16.2
+    - python3 -m venv venv
+    - venv/bin/pip install --upgrade pip
+    - venv/bin/pip install cibuildwheel==2.16.2
   run_cibuildwheel_script:
-    - bin/cibw.sh
+    - venv/bin/cibuildwheel --platform macos
   wheels_artifacts:
     path: "wheelhouse/*"
diff --git a/.github/workflows/buildwheel.yml b/.github/workflows/buildwheel.yml
index 88f79c62..536d00c9 100644
--- a/.github/workflows/buildwheel.yml
+++ b/.github/workflows/buildwheel.yml
@@ -10,7 +10,7 @@ jobs:
     strategy:
       fail-fast: false
       matrix:
-        os: [ubuntu-20.04, windows-2019, macos-12]
+        os: [ubuntu-20.04, windows-2019, macos-13]
 
     steps:
       - uses: actions/checkout@v4
@@ -31,6 +31,16 @@ jobs:
           path-type: inherit
         if: ${{ matrix.os == 'windows-2019' }}
 
+        # Install pkgconfig on Windows from choco rather than from msys and
+        # avoid using the Strawberry one.
+      - run: choco install -y --stoponfirstfailure --checksum 6004DF17818F5A6DBF19CB335CC92702 pkgconfiglite
+        if: ${{ matrix.os == 'windows-2019' }}
+
+        # We have to set this here rather than in the cibuildwheel config
+        # This is probably something to do with \ vs / in paths...
+      - run: echo "PKG_CONFIG_PATH=${{ github.workspace }}/.local/lib/pkgconfig" >> $env:GITHUB_ENV
+        if: ${{ matrix.os == 'windows-2019' }}
+
       - name: Build wheels
         uses: pypa/cibuildwheel@v2.16.5
         env:
@@ -45,7 +55,7 @@ jobs:
 
   build_sdist:
     name: Build sdist
-    runs-on: ubuntu-20.04
+    runs-on: ubuntu-22.04
 
     steps:
       - uses: actions/checkout@v4
@@ -54,6 +64,11 @@ jobs:
         with:
           python-version: '3.12'
 
+      - run: sudo apt-get update
+      - run: sudo apt-get install libgmp-dev libmpfr-dev xz-utils ninja-build
+      - run: curl -O -L https://www.flintlib.org/flint-3.1.0.tar.gz
+      - run: tar -xzf flint-3.1.0.tar.gz
+      - run: cd flint-3.1.0 && ./configure --disable-static && make -j4 && sudo make install
       - run: pip install build
       - run: python -m build --sdist
 
@@ -91,7 +106,7 @@ jobs:
     strategy:
       fail-fast: false
       matrix:
-        os: [ubuntu-20.04, windows-2019, macos-12]
+        os: [ubuntu-20.04, windows-2019, macos-13]
         python-version: ['3.9', '3.10', '3.11', '3.12']
 
     steps:
diff --git a/.gitignore b/.gitignore
index 213e156f..0f4570f3 100644
--- a/.gitignore
+++ b/.gitignore
@@ -18,3 +18,4 @@ MANIFEST
 .python-version
 *.DS_Store
 .venv
+.hypothesis
diff --git a/bin/activate b/bin/activate
index 83f5d452..81e1eead 100644
--- a/bin/activate
+++ b/bin/activate
@@ -1,4 +1,3 @@
 export C_INCLUDE_PATH=$(pwd)/.local/include
 export LIBRARY_PATH=$(pwd)/.local/lib
 export LD_LIBRARY_PATH=$(pwd)/.local/lib
-export PYTHONPATH=$(pwd)/src
diff --git a/bin/cibw.sh b/bin/cibw.sh
deleted file mode 100755
index 23a70498..00000000
--- a/bin/cibw.sh
+++ /dev/null
@@ -1,18 +0,0 @@
-#!/usr/bin/env bash
-#
-# This script can be used to test cibuildwheel locally on OSX/Linux
-#
-# It is also worth commenting out the BEFORE_ALL line to build GMP etc after you have
-# built those once because that is by far the slowest step.
-#
-
-rm -f wheelhouse/*
-
-# export CIBW_ARCHS_MACOS="x86_64"
-export CIBW_ARCHS_MACOS="arm64"
-
-export CIBW_TEST_COMMAND="python -m flint.test"  # override setting in pyproject.toml
-
-# cibuildwheel --platform linux
-# cibuildwheel --platform windows
-cibuildwheel --platform macos
diff --git a/bin/pip_install_ubuntu.sh b/bin/pip_install_ubuntu.sh
index dce9b9d0..b28e31e7 100755
--- a/bin/pip_install_ubuntu.sh
+++ b/bin/pip_install_ubuntu.sh
@@ -35,7 +35,7 @@ PYTHON_FLINT=$1
 
 # First install their dependencies and build dependencies
 sudo apt-get update
-sudo apt-get install libgmp-dev libmpfr-dev xz-utils
+sudo apt-get install libgmp-dev libmpfr-dev xz-utils ninja-build
 
 if [ -z "$FLINT_GIT" ]; then
     # Install from release tarball
diff --git a/meson.build b/meson.build
new file mode 100644
index 00000000..b4fe7f83
--- /dev/null
+++ b/meson.build
@@ -0,0 +1,19 @@
+project('python-flint', 'cython', 'c')
+
+py = import('python').find_installation(pure: false)
+dep_py = py.dependency()
+
+cc = meson.get_compiler('c')
+
+gmp_dep = dependency('gmp')
+mpfr_dep = dependency('mpfr')
+flint_dep = dependency('flint')
+
+# flint.pc was missing -lflint until Flint 3.1.0
+if flint_dep.version().version_compare('<3.1')
+  flint_dep = cc.find_library('flint')
+endif
+
+pyflint_deps = [dep_py, gmp_dep, mpfr_dep, flint_dep]
+
+subdir('src/flint')
diff --git a/pyproject.toml b/pyproject.toml
index 19d18a8a..e29f7ccf 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -1,8 +1,6 @@
 [build-system]
-requires = ["setuptools",
-            "numpy; sys_platform == 'win32' and python_version < '3.12'",
-            "Cython>=3"]
-build-backend = "setuptools.build_meta"
+requires = ["meson-python", "cython"]
+build-backend = "mesonpy"
 
 [project]
 name = "python-flint"
@@ -21,6 +19,27 @@ classifiers = [
 file = "README.md"
 content-type = "text/markdown"
 
+[tool.spin]
+package = "flint"
+
+[tool.spin.commands]
+
+"Build" = [
+    "spin.cmds.meson.build",
+    "spin.cmds.meson.test",
+    "spin.cmds.build.sdist",
+    "spin.cmds.pip.install",
+]
+"Documentation" = [
+    "spin.cmds.meson.docs",
+]
+"Environments" = [
+    "spin.cmds.meson.shell",
+    "spin.cmds.meson.ipython",
+    "spin.cmds.meson.python",
+    "spin.cmds.meson.run",
+]
+
 [tool.cibuildwheel]
 build = "cp39-* cp310-* cp311-* cp312-*"
 skip = "*-win32 *-manylinux_i686 *-musllinux_*"
@@ -28,11 +47,18 @@ manylinux-x86_64-image = "manylinux2014"
 manylinux-i686-image = "manylinux2014"
 test-command = "python -c \"import flint; print(str(flint.fmpz(2)))\""
 
-[tool.cibuildwheel.environment]
-# bin/build_dependencies_unix.sh places headers and shared libraries under .local
-C_INCLUDE_PATH = "$(pwd)/.local/include/"
-LIBRARY_PATH = "$(pwd)/.local/lib/"
+[tool.cibuildwheel.linux.environment]
+# LD_LIBRARY_PATH is needed by auditwheel
 LD_LIBRARY_PATH = "$(pwd)/.local/lib:$LD_LIBRARY_PATH"
+PKG_CONFIG_PATH = "$(pwd)/.local/lib/pkgconfig"
+
+[tool.cibuildwheel.macos.environment]
+PKG_CONFIG_PATH = "$(pwd)/.local/lib/pkgconfig"
+
+[tool.cibuildwheel.windows.environment]
+# Setting PKG_CONFIG_PATH here breaks pkgconfig for some reason...
+# We set it in the CI workflow instead.
+# PKG_CONFIG_PATH = "$(pwd)/.local/lib/pkgconfig:$PKG_CONFIG_PATH"
 
 [tool.cibuildwheel.linux]
 before-all = "bin/cibw_before_all_linux.sh"
@@ -44,6 +70,3 @@ before-all = "bin/cibw_before_all_macosx_$(uname -m).sh"
 before-all = "C:\\msys64\\usr\\bin\\bash bin/cibw_before_all_windows.sh"
 before-build = "pip install delvewheel && C:\\msys64\\usr\\bin\\bash bin/cibw_before_build_windows.sh"
 repair-wheel-command = "bin\\cibw_repair_wheel_command_windows.bat {dest_dir} {wheel}"
-
-[tool.cibuildwheel.windows.environment]
-PYTHON_FLINT_MINGW64 = "true"
diff --git a/src/flint/flint_base/meson.build b/src/flint/flint_base/meson.build
new file mode 100644
index 00000000..6c6943d7
--- /dev/null
+++ b/src/flint/flint_base/meson.build
@@ -0,0 +1,26 @@
+pkgdir = 'flint/flint_base'
+
+pyfiles = [
+  '__init__.py',
+]
+
+exts = [
+  'flint_base',
+  'flint_context',
+]
+
+py.install_sources(
+  pyfiles,
+  pure: false,
+  subdir: pkgdir,
+)
+
+foreach ext : exts
+  py.extension_module(
+    ext,
+    ext + '.pyx',
+    dependencies: pyflint_deps,
+    install: true,
+    subdir: pkgdir,
+  )
+endforeach
diff --git a/src/flint/functions/meson.build b/src/flint/functions/meson.build
new file mode 100644
index 00000000..80f1f869
--- /dev/null
+++ b/src/flint/functions/meson.build
@@ -0,0 +1,23 @@
+pyfiles = [
+  '__init__.py',
+]
+
+exts = [
+  'showgood',
+]
+
+py.install_sources(
+  pyfiles,
+  pure: false,
+  subdir: 'flint/functions',
+)
+
+foreach ext : exts
+  py.extension_module(
+    ext,
+    ext + '.pyx',
+    dependencies: pyflint_deps,
+    install: true,
+    subdir: 'flint/functions',
+  )
+endforeach
diff --git a/src/flint/meson.build b/src/flint/meson.build
new file mode 100644
index 00000000..4ed3dc99
--- /dev/null
+++ b/src/flint/meson.build
@@ -0,0 +1,37 @@
+thisdir = 'flint'
+
+pyfiles = [
+  '__init__.py',
+]
+
+exts = [
+  'pyflint',
+]
+
+pkgs = [
+  'flint_base',
+  'types',
+  'functions',
+  'utils',
+  'test',
+]
+
+py.install_sources(
+  pyfiles,
+  pure: false,
+  subdir: thisdir,
+)
+
+foreach ext : exts
+  py.extension_module(
+    ext,
+    ext + '.pyx',
+    dependencies: pyflint_deps,
+    install: true,
+    subdir: thisdir,
+  )
+endforeach
+
+foreach pkg : pkgs
+  subdir(pkg)
+endforeach
diff --git a/src/flint/test/__main__.py b/src/flint/test/__main__.py
index 637fdb46..d16b0aa5 100644
--- a/src/flint/test/__main__.py
+++ b/src/flint/test/__main__.py
@@ -10,7 +10,7 @@
 import argparse
 
 import flint
-from flint.test.test import all_tests
+from flint.test.test_all import all_tests
 
 
 def run_tests(verbose=None):
diff --git a/src/flint/test/meson.build b/src/flint/test/meson.build
new file mode 100644
index 00000000..4aa245a1
--- /dev/null
+++ b/src/flint/test/meson.build
@@ -0,0 +1,13 @@
+thisdir = 'flint/test'
+
+pyfiles = [
+  '__init__.py',
+  '__main__.py',
+  'test_all.py',
+]
+
+py.install_sources(
+  pyfiles,
+  pure: false,
+  subdir: thisdir,
+)
diff --git a/src/flint/test/test.py b/src/flint/test/test_all.py
similarity index 100%
rename from src/flint/test/test.py
rename to src/flint/test/test_all.py
diff --git a/src/flint/types/meson.build b/src/flint/types/meson.build
new file mode 100644
index 00000000..bf8caec5
--- /dev/null
+++ b/src/flint/types/meson.build
@@ -0,0 +1,58 @@
+thisdir = 'flint/types'
+
+pyfiles = [
+  '__init__.py',
+]
+
+exts = [
+  'fmpz',
+  'fmpz_poly',
+  'fmpz_mat',
+  'fmpz_series',
+
+  'fmpq',
+  'fmpq_poly',
+  'fmpq_mat',
+  'fmpq_series',
+
+  'nmod',
+  'nmod_poly',
+  'nmod_mat',
+  'nmod_series',
+
+  'fmpz_mod',
+  'fmpz_mod_poly',
+  'fmpz_mod_mat',
+
+  'arf',
+
+  'arb',
+  'arb_poly',
+  'arb_mat',
+  'arb_series',
+
+  'acb',
+  'acb_poly',
+  'acb_mat',
+  'acb_series',
+
+  'dirichlet',
+
+  'fmpz_mpoly',
+]
+
+py.install_sources(
+  pyfiles,
+  pure: false,
+  subdir: thisdir,
+)
+
+foreach ext : exts
+  py.extension_module(
+    ext,
+    ext + '.pyx',
+    dependencies: pyflint_deps,
+    install: true,
+    subdir: thisdir,
+  )
+endforeach
diff --git a/src/flint/utils/meson.build b/src/flint/utils/meson.build
new file mode 100644
index 00000000..d05a2dd9
--- /dev/null
+++ b/src/flint/utils/meson.build
@@ -0,0 +1,24 @@
+thisdir = 'flint/utils'
+
+pyfiles = [
+  '__init__.py',
+  'flint_exceptions.py',
+]
+
+exts = []
+
+py.install_sources(
+  pyfiles,
+  pure: false,
+  subdir: thisdir,
+)
+
+foreach ext : exts
+  py.extension_module(
+    ext,
+    ext + '.pyx',
+    dependencies: pyflint_deps,
+    install: true,
+    subdir: thisdir,
+  )
+endforeach