diff --git a/.github/workflows/pypi.yml b/.github/workflows/pypi.yml
index 8b1a309a96..6d2af206ed 100644
--- a/.github/workflows/pypi.yml
+++ b/.github/workflows/pypi.yml
@@ -164,7 +164,7 @@ jobs:
       - name: Set up Python
         uses: actions/setup-python@a309ff8b426b58ec0e2a45f0f869d46889d02405 # v6.2.0
         with:
-          python-version: '3.11'
+          python-version: '3.12'
 
       - name: Install dependencies
         run: pip install --upgrade setuptools numpy versioneer wheel
@@ -204,7 +204,7 @@ jobs:
       - name: Set up Python
         uses: actions/setup-python@a309ff8b426b58ec0e2a45f0f869d46889d02405 # v6.2.0
         with:
-          python-version: '3.11'
+          python-version: '3.12'
 
       - name: Check SDist
         run: |
diff --git a/.github/workflows/slow-tests-issue.yml b/.github/workflows/slow-tests-issue.yml
index cb063eefd7..b5a35dc591 100644
--- a/.github/workflows/slow-tests-issue.yml
+++ b/.github/workflows/slow-tests-issue.yml
@@ -22,7 +22,7 @@ jobs:
       - name: Set up Python
         uses: actions/setup-python@a309ff8b426b58ec0e2a45f0f869d46889d02405 # v6.2.0
         with:
-          python-version: "3.11"
+          python-version: "3.12"
       - name: Trigger the script
         continue-on-error: true
         working-directory: scripts/slowest_tests
diff --git a/.github/workflows/test.yml b/.github/workflows/test.yml
index cbf9d142e3..3760b4e6b7 100644
--- a/.github/workflows/test.yml
+++ b/.github/workflows/test.yml
@@ -56,7 +56,7 @@ jobs:
     if: ${{ needs.changes.outputs.changes == 'true' }}
     strategy:
       matrix:
-        python-version: ["3.11", "3.14"]
+        python-version: ["3.12", "3.14"]
     steps:
       - uses: actions/checkout@de0fac2e4500dabe0009e67214ff5f5447ce83dd # v6.0.2
         with:
@@ -78,7 +78,7 @@ jobs:
       matrix:
         # default-mode: "NUMBA" is actually a no-op, to make sure we're testing default config settings
         default-mode: ["CVM", "NUMBA", "FAST_COMPILE"]
-        python-version: ["3.11", "3.14"]
+        python-version: ["3.12", "3.14"]
         os: ["ubuntu-latest"]
         install-jax: [0]
         install-torch: [0]
@@ -94,7 +94,7 @@ jobs:
           - [ "tensor rewriting", "tests/tensor/rewriting" ]
           - [ "tensor linalg", "tests/tensor/linalg" ]
         exclude:
-          - python-version: "3.11"
+          - python-version: "3.12"
             default-mode: "FAST_COMPILE"
         include:
           - part: ["doctests", "--doctest-modules pytensor --ignore=pytensor/misc/check_duplicate_key.py --ignore=pytensor/link --ignore=pytensor/ipython.py"]
@@ -117,7 +117,7 @@ jobs:
           - part: ["pytorch link", "tests/link/pytorch"]
             install-torch: 1
             default-mode: "CVM"
-            python-version: "3.11"
+            python-version: "3.12"
             os: "ubuntu-latest"
           - part: ["xtensor", "tests/xtensor"]
             install-xarray: 1
@@ -127,7 +127,7 @@ jobs:
           - part: ["mlx link", "tests/link/mlx"]
             install-mlx: 1
             default-mode: "CVM"
-            python-version: "3.11"
+            python-version: "3.12"
             os: "macos-15"
           - part: ["macos smoke test", "tests/tensor/test_elemwise.py tests/tensor/test_math_scipy.py tests/tensor/test_blas.py"]
             default-mode: "CVM"
@@ -223,7 +223,7 @@ jobs:
         with:
           fetch-depth: 0
           persist-credentials: false
-      - name: Set up Python 3.11
+      - name: Set up Python 3.12
         uses: mamba-org/setup-micromamba@add3a49764cedee8ee24e82dfde87f5bc2914462 # v2.0.7
         with:
           environment-name: pytensor-test
@@ -239,7 +239,7 @@ jobs:
           python -c 'import pytensor; print(pytensor.config.__str__(print_doc=False))'
           python -c 'import pytensor; assert pytensor.config.blas__ldflags != "", "Blas flags are empty"'
         env:
-          PYTHON_VERSION: 3.11
+          PYTHON_VERSION: 3.12
       - name: Download previous benchmark data
         uses: actions/cache@27d5ce7f107fe9357f9df03efb73ab90386fccae # v5.0.5
         with:
diff --git a/doc/environment.yml b/doc/environment.yml
index 50dd65df6b..8d3419e7a7 100644
--- a/doc/environment.yml
+++ b/doc/environment.yml
@@ -3,7 +3,7 @@ channels:
   - conda-forge
   - nodefaults
 dependencies:
-  - python=3.11
+  - python=3.12
   - gcc_linux-64
   - gxx_linux-64
   - numpy
diff --git a/environment-osx-arm64.yml b/environment-osx-arm64.yml
index 2424332e86..74d524466b 100644
--- a/environment-osx-arm64.yml
+++ b/environment-osx-arm64.yml
@@ -7,7 +7,7 @@ name: pytensor-dev
 channels:
   - conda-forge
 dependencies:
-  - python>=3.11
+  - python>=3.12
   - compilers
   - numpy>=2.0.0
   - scipy>=1,<2
diff --git a/environment.yml b/environment.yml
index 9ca4b350a1..4e28fe7b91 100644
--- a/environment.yml
+++ b/environment.yml
@@ -7,7 +7,7 @@ name: pytensor-dev
 channels:
   - conda-forge
 dependencies:
-  - python>=3.11
+  - python>=3.12
   - compilers
   - numpy>=2.0.0
   - scipy>=1,<2
diff --git a/pyproject.toml b/pyproject.toml
index 1edd5034ec..ea9d0728f8 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -10,7 +10,7 @@ build-backend = "setuptools.build_meta"
 [project]
 name = "pytensor"
 dynamic = ['version']
-requires-python = ">=3.11,<3.15"
+requires-python = ">=3.12,<3.15"
 authors = [{ name = "pymc-devs", email = "pymc.devs@gmail.com" }]
 description = "Optimizing compiler for evaluating mathematical expressions on CPUs and GPUs."
 readme = "README.rst"
@@ -30,7 +30,6 @@ classifiers = [
     "Operating System :: Unix",
     "Operating System :: MacOS",
     "Programming Language :: Python :: 3",
-    "Programming Language :: Python :: 3.11",
     "Programming Language :: Python :: 3.12",
     "Programming Language :: Python :: 3.13",
     "Programming Language :: Python :: 3.14",
@@ -169,7 +168,7 @@ lines-after-imports = 2
 
 
 [tool.mypy]
-python_version = "3.11"
+python_version = "3.12"
 ignore_missing_imports = true
 strict_equality = true
 warn_redundant_casts = true
diff --git a/pytensor/gradient.py b/pytensor/gradient.py
index ccc89fffb9..7eb7150fef 100644
--- a/pytensor/gradient.py
+++ b/pytensor/gradient.py
@@ -48,7 +48,7 @@ def _match_tangent_dtype(var: Variable, tangent: Variable) -> Variable:
 
 
 # TODO: Add `overload` variants
-def as_list_or_tuple(
+def as_list_or_tuple[V: Variable | None](
     use_list: bool, use_tuple: bool, outputs: V | Sequence[V]
 ) -> V | list[V] | tuple[V, ...]:
     """Return either a single object or a list/tuple of objects.
diff --git a/pytensor/graph/basic.py b/pytensor/graph/basic.py
index 32601cdb3e..b58c8635c9 100644
--- a/pytensor/graph/basic.py
+++ b/pytensor/graph/basic.py
@@ -108,7 +108,7 @@ def dprint(self, **kwargs):
         return debugprint(self, **kwargs)
 
 
-class Apply(Node, Generic[OpType]):
+class Apply(Node, Generic[OpType]):  # noqa: UP046
     """A `Node` representing the application of an operation to inputs.
 
     Basically, an `Apply` instance is an object that represents the
@@ -345,7 +345,7 @@ def params_type(self):
         return self.op.params_type
 
 
-class Variable(Node, Generic[_TypeType, OptionalApplyType]):
+class Variable(Node, Generic[_TypeType, OptionalApplyType]):  # noqa: UP046
     r"""
     A :term:`Variable` is a node in an expression graph that represents a
     variable.
@@ -677,7 +677,7 @@ def clone(self, **kwargs):
         return cp
 
 
-class NominalVariable(Generic[_TypeType, _IdType], AtomicVariable[_TypeType]):
+class NominalVariable(Generic[_TypeType, _IdType], AtomicVariable[_TypeType]):  # noqa: UP046
     """A variable that enables alpha-equivalent comparisons."""
 
     __instances__: dict[tuple["Type", Hashable], "NominalVariable"] = {}
diff --git a/pytensor/graph/rewriting/unify.py b/pytensor/graph/rewriting/unify.py
index 195dd18564..c0b48f8aad 100644
--- a/pytensor/graph/rewriting/unify.py
+++ b/pytensor/graph/rewriting/unify.py
@@ -14,7 +14,7 @@
 from dataclasses import dataclass
 from numbers import Number
 from types import UnionType
-from typing import Any, TypeAlias
+from typing import Any
 
 import numpy as np
 from cons.core import ConsError, _car, _cdr
@@ -262,7 +262,7 @@ class LiteralString:
     value: str
 
 
-OpPatternOpTypeType: TypeAlias = type[Op] | tuple[type[Op], ...] | UnionType
+type OpPatternOpTypeType = type[Op] | tuple[type[Op], ...] | UnionType
 
 
 @dataclass(unsafe_hash=True)
diff --git a/pytensor/graph/traversal.py b/pytensor/graph/traversal.py
index 08b0bc2fd8..fd18b0a2b4 100644
--- a/pytensor/graph/traversal.py
+++ b/pytensor/graph/traversal.py
@@ -20,7 +20,7 @@
 
 
 @overload
-def walk(
+def walk[T: Node](
     nodes: Iterable[T],
     expand: Callable[[T], Iterable[T] | None],
     bfs: bool = True,
@@ -29,7 +29,7 @@ def walk(
 
 
 @overload
-def walk(
+def walk[T: Node](
     nodes: Iterable[T],
     expand: Callable[[T], Iterable[T] | None],
     bfs: bool,
@@ -37,7 +37,7 @@ def walk(
 ) -> Generator[NodeAndChildren, None, None]: ...
 
 
-def walk(
+def walk[T: Node](
     nodes: Iterable[T],
     expand: Callable[[T], Iterable[T] | None],
     bfs: bool = True,
@@ -511,7 +511,7 @@ def truncated_graph_inputs(
     return truncated_inputs
 
 
-def walk_toposort(
+def walk_toposort[T: Node](
     graphs: Iterable[T],
     deps: Callable[[T], Iterable[T] | None],
 ) -> Generator[T, None, None]:
@@ -579,7 +579,7 @@ def compute_deps_cache(obj, deps_cache=deps_cache):
         raise ValueError("graph contains cycles")
 
 
-def general_toposort(
+def general_toposort[T: Node](
     outputs: Iterable[T],
     deps: Callable[[T], Iterable[T] | None],
     compute_deps_cache: Callable[[T], Iterable[T] | None] | None = None,
diff --git a/pytensor/graph/type.py b/pytensor/graph/type.py
index d4d800716d..a9a961564c 100644
--- a/pytensor/graph/type.py
+++ b/pytensor/graph/type.py
@@ -9,7 +9,7 @@
 D = TypeVar("D")
 
 
-class Type(MetaObject, Generic[D]):
+class Type(MetaObject, Generic[D]):  # noqa: UP046
     """
     Interface specification for variable type instances.
 
@@ -23,12 +23,12 @@ class Type(MetaObject, Generic[D]):
 
     """
 
-    variable_type: TypeAlias = Variable
+    variable_type: TypeAlias = Variable  # noqa: UP040
     """
     The `Type` that will be created by a call to `Type.make_variable`.
     """
 
-    constant_type: TypeAlias = Constant
+    constant_type: TypeAlias = Constant  # noqa: UP040
     """
     The `Type` that will be created by a call to `Type.make_constant`.
     """
diff --git a/pytensor/graph/utils.py b/pytensor/graph/utils.py
index 8e8eb440d2..d24003230b 100644
--- a/pytensor/graph/utils.py
+++ b/pytensor/graph/utils.py
@@ -73,7 +73,7 @@ def simple_extract_stack(
     return trace
 
 
-def add_tag_trace(thing: T, user_line: int | None = None) -> T:
+def add_tag_trace[T: "Apply" | "Variable"](thing: T, user_line: int | None = None) -> T:
     """Add tag.trace to a node or variable.
 
     The argument is returned after being affected (inplace).
diff --git a/pytensor/link/numba/dispatch/linalg/solvers/lu_solve.py b/pytensor/link/numba/dispatch/linalg/solvers/lu_solve.py
index 0939807fd8..b737e9d5d6 100644
--- a/pytensor/link/numba/dispatch/linalg/solvers/lu_solve.py
+++ b/pytensor/link/numba/dispatch/linalg/solvers/lu_solve.py
@@ -1,5 +1,5 @@
 from collections.abc import Callable
-from typing import Literal, TypeAlias
+from typing import Literal
 
 import numpy as np
 from numba.core.extending import overload
@@ -21,7 +21,7 @@
 )
 
 
-_Trans: TypeAlias = Literal[0, 1, 2]
+type _Trans = Literal[0, 1, 2]
 
 
 def _getrs(
diff --git a/pytensor/scalar/basic.py b/pytensor/scalar/basic.py
index d3a7f2f650..42f1545026 100644
--- a/pytensor/scalar/basic.py
+++ b/pytensor/scalar/basic.py
@@ -15,7 +15,7 @@
 from collections.abc import Callable
 from itertools import chain
 from textwrap import dedent
-from typing import Any, TypeAlias
+from typing import Any
 
 import numpy as np
 
@@ -790,7 +790,7 @@ def get_scalar_type(dtype, cache: dict[str, ScalarType] = {}) -> ScalarType:
 complex64: ScalarType = get_scalar_type("complex64")
 complex128: ScalarType = get_scalar_type("complex128")
 
-_ScalarTypes: TypeAlias = tuple[ScalarType, ...]
+type _ScalarTypes = tuple[ScalarType, ...]
 int_types: _ScalarTypes = (int8, int16, int32, int64)
 uint_types: _ScalarTypes = (uint8, uint16, uint32, uint64)
 float_types: _ScalarTypes = (float16, float32, float64)
diff --git a/pytensor/tensor/random/variable.py b/pytensor/tensor/random/variable.py
index 136322bf27..b7eb931b54 100644
--- a/pytensor/tensor/random/variable.py
+++ b/pytensor/tensor/random/variable.py
@@ -1,7 +1,6 @@
 import copy
 import warnings
 from functools import wraps
-from typing import TypeAlias
 
 import numpy as np
 
@@ -12,7 +11,7 @@
 from pytensor.tensor.variable import TensorVariable
 
 
-RNG_AND_DRAW: TypeAlias = tuple["RandomGeneratorVariable", TensorVariable]
+type RNG_AND_DRAW = tuple["RandomGeneratorVariable", TensorVariable]
 
 
 def warn_reuse(func):
diff --git a/pytensor/tensor/reshape.py b/pytensor/tensor/reshape.py
index b25308fccc..aab187a4ef 100644
--- a/pytensor/tensor/reshape.py
+++ b/pytensor/tensor/reshape.py
@@ -1,6 +1,5 @@
 from collections.abc import Iterable, Sequence
 from itertools import pairwise
-from typing import TypeAlias
 
 import numpy as np
 from numpy.lib._array_utils_impl import normalize_axis_index, normalize_axis_tuple
@@ -16,9 +15,7 @@
 from pytensor.tensor.variable import TensorVariable
 
 
-ShapeValueType: TypeAlias = (
-    int | np.integer | ScalarVariable | TensorVariable | np.ndarray
-)
+type ShapeValueType = int | np.integer | ScalarVariable | TensorVariable | np.ndarray
 
 
 class JoinDims(Op):
diff --git a/pytensor/tensor/subtensor.py b/pytensor/tensor/subtensor.py
index f180d2e9c6..70fbc9fc12 100644
--- a/pytensor/tensor/subtensor.py
+++ b/pytensor/tensor/subtensor.py
@@ -71,7 +71,7 @@
 T = TypeVar("T")
 
 
-def flatten_index_variables(
+def flatten_index_variables[T](
     idx_vars: Sequence[T | None | slice],
 ) -> tuple[list[int | slice], list[T]]:
     counter = 0
@@ -99,7 +99,7 @@ def flatten_index_variables(
     return idx_list, flat_vars
 
 
-def unflatten_index_variables(
+def unflatten_index_variables[T](
     flat_indices: Sequence[T],
     idx_list: Sequence[slice | int],
 ) -> tuple[slice | T, ...]:
diff --git a/pytensor/xtensor/random/variable.py b/pytensor/xtensor/random/variable.py
index e511753194..5f84f85881 100644
--- a/pytensor/xtensor/random/variable.py
+++ b/pytensor/xtensor/random/variable.py
@@ -1,5 +1,4 @@
 import copy
-from typing import TypeAlias
 
 import numpy as np
 
@@ -17,7 +16,7 @@
 from pytensor.xtensor.type import XTensorVariable
 
 
-XRNG_AND_DRAW: TypeAlias = tuple["XRandomGeneratorVariable", XTensorVariable]
+type XRNG_AND_DRAW = tuple["XRandomGeneratorVariable", XTensorVariable]
 
 __all__ = [
     "XRandomGeneratorSharedVariable",