diff --git a/build_tools/azure/install.sh b/build_tools/azure/install.sh
index 26b184d6f7d1d..1c76a7a4aa5d3 100755
--- a/build_tools/azure/install.sh
+++ b/build_tools/azure/install.sh
@@ -83,11 +83,11 @@ python_environment_install_and_activate() {
         echo "Installing development dependency wheels"
         dev_anaconda_url=https://pypi.anaconda.org/scipy-wheels-nightly/simple
         pip install --pre --upgrade --timeout=60 --extra-index $dev_anaconda_url numpy pandas scipy
-        echo "Installing Cython from PyPI enabling pre-releases"
-        pip install --pre cython
-        echo "Installing joblib master"
+        echo "Installing Cython from latest sources"
+        pip install https://github.com/cython/cython/archive/master.zip
+        echo "Installing joblib from latest sources"
         pip install https://github.com/joblib/joblib/archive/master.zip
-        echo "Installing pillow master"
+        echo "Installing pillow from latest sources"
         pip install https://github.com/python-pillow/Pillow/archive/main.zip
     fi
 }
diff --git a/sklearn/_build_utils/__init__.py b/sklearn/_build_utils/__init__.py
index 6828192aaf4a5..755171ee770c4 100644
--- a/sklearn/_build_utils/__init__.py
+++ b/sklearn/_build_utils/__init__.py
@@ -40,6 +40,7 @@ def cythonize_extensions(extension):
     """Check that a recent Cython is available and cythonize extensions"""
     _check_cython_version()
     from Cython.Build import cythonize
+    import Cython
 
     # Fast fail before cythonization if compiler fails compiling basic test
     # code even without OpenMP
@@ -70,20 +71,37 @@ def cythonize_extensions(extension):
         os.environ.get("SKLEARN_ENABLE_DEBUG_CYTHON_DIRECTIVES", "0") != "0"
     )
 
+    compiler_directives = {
+        "language_level": 3,
+        "boundscheck": cython_enable_debug_directives,
+        "wraparound": False,
+        "initializedcheck": False,
+        "nonecheck": False,
+        "cdivision": True,
+    }
+
+    # TODO: once Cython 3 is released and we require Cython>=3 we should get
+    # rid of the `legacy_implicit_noexcept` directive.
+    # This should mostly consist in:
+    #
+    #   - ensuring nogil is at the end of function signature,
+    #   e.g. replace "nogil except -1" by "except -1 nogil".
+    #
+    #   - "noexcept"-qualifying Cython and externalized C interfaces
+    #   which aren't raising nor propagating exceptions.
+    #   See: https://cython.readthedocs.io/en/latest/src/userguide/language_basics.html#error-return-values  # noqa
+    #
+    # See: https://github.com/cython/cython/issues/5088 for more details
+    if parse(Cython.__version__) > parse("3.0.0a11"):
+        compiler_directives["legacy_implicit_noexcept"] = True
+
     return cythonize(
         extension,
         nthreads=n_jobs,
         compile_time_env={
             "SKLEARN_OPENMP_PARALLELISM_ENABLED": sklearn._OPENMP_SUPPORTED
         },
-        compiler_directives={
-            "language_level": 3,
-            "boundscheck": cython_enable_debug_directives,
-            "wraparound": False,
-            "initializedcheck": False,
-            "nonecheck": False,
-            "cdivision": True,
-        },
+        compiler_directives=compiler_directives,
     )
 
 
diff --git a/sklearn/neighbors/_binary_tree.pxi b/sklearn/neighbors/_binary_tree.pxi
index 415fa0292fcda..00b5b3c2758d3 100644
--- a/sklearn/neighbors/_binary_tree.pxi
+++ b/sklearn/neighbors/_binary_tree.pxi
@@ -846,7 +846,7 @@ cdef class BinaryTree:
         # with numbers of points between leaf_size and 2 * leaf_size
         self.n_levels = int(
             np.log2(fmax(1, (n_samples - 1) / self.leaf_size)) + 1)
-        self.n_nodes = (2 ** self.n_levels) - 1
+        self.n_nodes = <int> (2 ** self.n_levels) - 1
 
         # allocate arrays for storage
         self.idx_array = np.arange(n_samples, dtype=ITYPE)
diff --git a/sklearn/neighbors/_quad_tree.pyx b/sklearn/neighbors/_quad_tree.pyx
index 3d2c306a38177..a7607cb56e0eb 100644
--- a/sklearn/neighbors/_quad_tree.pyx
+++ b/sklearn/neighbors/_quad_tree.pyx
@@ -52,7 +52,7 @@ cdef class _QuadTree:
         # Parameters of the tree
         self.n_dimensions = n_dimensions
         self.verbose = verbose
-        self.n_cells_per_cell = 2 ** self.n_dimensions
+        self.n_cells_per_cell = <int> (2 ** self.n_dimensions)
 
         # Inner structures
         self.max_depth = 0
diff --git a/sklearn/tree/_tree.pyx b/sklearn/tree/_tree.pyx
index 68cb2475d3868..e5d983b1344bf 100644
--- a/sklearn/tree/_tree.pyx
+++ b/sklearn/tree/_tree.pyx
@@ -155,7 +155,7 @@ cdef class DepthFirstTreeBuilder(TreeBuilder):
         cdef int init_capacity
 
         if tree.max_depth <= 10:
-            init_capacity = (2 ** (tree.max_depth + 1)) - 1
+            init_capacity = <int> (2 ** (tree.max_depth + 1)) - 1
         else:
             init_capacity = 2047