diff --git a/.github/workflows/build_wheels.yaml b/.github/workflows/build_wheels.yaml
new file mode 100644
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+++ b/.github/workflows/build_wheels.yaml
@@ -0,0 +1,135 @@
+name: Build
+
+# TODO: only run on published releases
+# on:
+#   release:
+#     types: [published]
+on: [pull_request]
+
+jobs:
+  build_wheels:
+    name: Build wheels on ${{ matrix.os }}
+    runs-on: ${{ matrix.os }}
+    strategy:
+      fail-fast: false
+      matrix:
+        # macos-13 is an intel runner, macos-14 is apple silicon
+        os: [
+          ubuntu-latest,
+          ubuntu-24.04-arm,
+          # Failing, probably need to:
+          # - read https://github.com/mesonbuild/meson-python/issues/222
+          # - maybe try with https://github.com/numpy/numpy/blob/71eebaf8513dfd6ed40b0c689702d81e3f6f2527/.github/workflows/wheels.yml#L133
+          # - maybe try with https://github.com/matplotlib/matplotlib/blob/5054100eaf8b49cfd8d42cac9c224f9f5dd92508/.github/workflows/cibuildwheel.yml#L81
+          windows-2022,
+          # # windows-latest is moving target at the moment
+          # windows-latest,
+          # To make this work, likely need some more trickery, see:
+          # - https://github.com/matplotlib/matplotlib/blob/5054100eaf8b49cfd8d42cac9c224f9f5dd92508/pyproject.toml#L89
+          # windows-11-arm,
+          # Maybe something crazy required,
+          # see numpy's fun https://github.com/numpy/numpy/blob/main/.github/windows_arm64_steps/action.yml
+          macos-13,
+          macos-14,
+        ]
+
+    steps:
+      - uses: actions/checkout@v5
+
+      - name: Setup Python
+        if: ${{ startsWith(matrix.os, 'windows') }}
+        uses: actions/setup-python@v5
+        with:
+          python-version: '3.x'
+
+      # Maybe not necessary, source:
+      # https://dvdhrm.github.io/2021/04/21/meson-msvc-github-actions/
+      # and
+      # https://github.com/numpy/numpy/blob/71eebaf8513dfd6ed40b0c689702d81e3f6f2527/.github/workflows/wheels.yml#L123
+      - name: Setup MSVC developer shell (32-bit)
+        if: ${{ matrix.os == 'windows-2022' }}
+        uses: bus1/cabuild/action/msdevshell@v1
+        with:
+          architecture: x64
+
+      - name: Install Fortran compiler
+        # When building from source, ensure we have a Fortran compiler
+        if: ${{ startsWith(matrix.os, 'macos') }}
+        uses: fortran-lang/setup-fortran@v1
+        id: setup-fortran
+        with:
+          # TODO: figure out whether we need/want to use other compilers too
+          compiler: "gcc"
+          version: "13"
+
+      - name: Set macOS-13 specific flags
+        if: matrix.os == 'macos-13'
+        run: |
+          echo "MACOSX_DEPLOYMENT_TARGET=13.0" >> "$GITHUB_ENV"
+
+      - name: Set macOS-14 specific flags
+        if: matrix.os == 'macos-14'
+        run: |
+          echo "MACOSX_DEPLOYMENT_TARGET=14.0" >> "$GITHUB_ENV"
+
+      - name: Build wheels
+        uses: pypa/cibuildwheel@v3.1.4
+        # env:
+        #   CIBW_SOME_OPTION: value
+        #   ...
+        with:
+          package-dir: .
+          output-dir: wheelhouse
+          config-file: "{package}/pyproject.toml"
+
+      - uses: actions/upload-artifact@v4
+        with:
+          name: cibw-wheels-${{ matrix.os }}-${{ strategy.job-index }}
+          path: wheelhouse/*.whl
+
+  make_sdist:
+    name: Make source distribution
+    runs-on: "ubuntu-latest"
+
+    steps:
+      - name: Check out repository
+        uses: actions/checkout@v4
+        with:
+          fetch-depth: 0
+
+      - uses: ./.github/actions/setup
+        with:
+          python-version: ${{ matrix.python-version }}
+          uv-dependency-install-flags: "--all-extras --group dev"
+
+      - name: Create source distribution
+        run: uv build --sdist
+
+      - name: Upload the source distribution artefact
+        uses: actions/upload-artifact@v4
+        with:
+          name: cibw-sdist
+          path: dist/*.tar.gz
+
+  deploy-pypi:
+    needs: [build_wheels, make_sdist]
+    # Having an environment for deployment is strongly recommend by PyPI
+    # https://docs.pypi.org/trusted-publishers/adding-a-publisher/#github-actions
+    # You can comment this line out if you don't want it.
+    # # TODO: turn back on when we only run this on main
+    # environment: deploy
+    # permissions:
+    #   # this permission is mandatory for trusted publishing with PyPI
+    #   id-token: write
+    runs-on: ubuntu-latest
+    steps:
+      - name: Download artefacts
+        uses: actions/download-artifact@v5
+        with:
+          pattern: cibw-*
+          path: dist
+          merge-multiple: true
+      - name: Publish to PyPI
+        run: |
+          ls dist
+          # uv publish