diff --git a/.github/workflows/misc.yml b/.github/workflows/misc.yml
index 1890488008..ade350aaa7 100644
--- a/.github/workflows/misc.yml
+++ b/.github/workflows/misc.yml
@@ -24,7 +24,7 @@ jobs:
       matrix:
         python-version: ["3.10"]
         install: ['pip']
-        check: ['style', 'doctest']
+        check: ['style', 'doctest', 'typing']
         pip-flags: ['']
         depends: ['REQUIREMENTS']
     env:
diff --git a/.pre-commit-config.yaml b/.pre-commit-config.yaml
index e99b9570d6..addd5f5634 100644
--- a/.pre-commit-config.yaml
+++ b/.pre-commit-config.yaml
@@ -25,3 +25,15 @@ repos:
     hooks:
       - id: flake8
         exclude: "^(doc|nisext|tools)/"
+  - repo: https://github.com/pre-commit/mirrors-mypy
+    rev: v0.991
+    hooks:
+      - id: mypy
+        # Sync with project.optional-dependencies.typing
+        additional_dependencies:
+          - pytest
+          - types-setuptools
+          - types-Pillow
+          - pydicom
+        # Sync with tool.mypy['exclude']
+        exclude: "^(doc|nisext|tools)/|.*/tests/"
diff --git a/nibabel/analyze.py b/nibabel/analyze.py
index e165112259..fc44693bc6 100644
--- a/nibabel/analyze.py
+++ b/nibabel/analyze.py
@@ -81,6 +81,9 @@
 can be loaded with and without a default flip, so the saved zoom will not
 constrain the affine.
 """
+from __future__ import annotations
+
+from typing import Type
 
 import numpy as np
 
@@ -88,7 +91,7 @@
 from .arraywriters import ArrayWriter, WriterError, get_slope_inter, make_array_writer
 from .batteryrunners import Report
 from .fileholders import copy_file_map
-from .spatialimages import HeaderDataError, HeaderTypeError, SpatialImage
+from .spatialimages import HeaderDataError, HeaderTypeError, SpatialHeader, SpatialImage
 from .volumeutils import (
     apply_read_scaling,
     array_from_file,
@@ -131,7 +134,7 @@
     ('glmax', 'i4'),
     ('glmin', 'i4'),
 ]
-data_history_dtd = [
+data_history_dtd: list[tuple[str, str] | tuple[str, str, tuple[int, ...]]] = [
     ('descrip', 'S80'),
     ('aux_file', 'S24'),
     ('orient', 'S1'),
@@ -172,7 +175,7 @@
 data_type_codes = make_dt_codes(_dtdefs)
 
 
-class AnalyzeHeader(LabeledWrapStruct):
+class AnalyzeHeader(LabeledWrapStruct, SpatialHeader):
     """Class for basic analyze header
 
     Implements zoom-only setting of affine transform, and no image
@@ -892,11 +895,11 @@ def may_contain_header(klass, binaryblock):
 class AnalyzeImage(SpatialImage):
     """Class for basic Analyze format image"""
 
-    header_class = AnalyzeHeader
+    header_class: Type[AnalyzeHeader] = AnalyzeHeader
     _meta_sniff_len = header_class.sizeof_hdr
-    files_types = (('image', '.img'), ('header', '.hdr'))
-    valid_exts = ('.img', '.hdr')
-    _compressed_suffixes = ('.gz', '.bz2', '.zst')
+    files_types: tuple[tuple[str, str], ...] = (('image', '.img'), ('header', '.hdr'))
+    valid_exts: tuple[str, ...] = ('.img', '.hdr')
+    _compressed_suffixes: tuple[str, ...] = ('.gz', '.bz2', '.zst')
 
     makeable = True
     rw = True
diff --git a/nibabel/benchmarks/bench_arrayproxy_slicing.py b/nibabel/benchmarks/bench_arrayproxy_slicing.py
index d313a7db5e..958923d7ea 100644
--- a/nibabel/benchmarks/bench_arrayproxy_slicing.py
+++ b/nibabel/benchmarks/bench_arrayproxy_slicing.py
@@ -26,7 +26,7 @@
 
 # if memory_profiler is installed, we get memory usage results
 try:
-    from memory_profiler import memory_usage
+    from memory_profiler import memory_usage  # type: ignore
 except ImportError:
     memory_usage = None
 
diff --git a/nibabel/brikhead.py b/nibabel/brikhead.py
index 470ed16664..54b6d021f3 100644
--- a/nibabel/brikhead.py
+++ b/nibabel/brikhead.py
@@ -27,7 +27,6 @@
 am aware) always be >= 1. This permits sub-brick indexing common in AFNI
 programs (e.g., example4d+orig'[0]').
 """
-
 import os
 import re
 from copy import deepcopy
diff --git a/nibabel/casting.py b/nibabel/casting.py
index a17a25a2c8..6232c615b5 100644
--- a/nibabel/casting.py
+++ b/nibabel/casting.py
@@ -3,6 +3,7 @@
 Most routines work round some numpy oddities in floating point precision and
 casting.  Others work round numpy casting to and from python ints
 """
+from __future__ import annotations
 
 import warnings
 from numbers import Integral
@@ -110,7 +111,7 @@ def float_to_int(arr, int_type, nan2zero=True, infmax=False):
 
 
 # Cache range values
-_SHARED_RANGES = {}
+_SHARED_RANGES: dict[tuple[type, type], tuple[np.number, np.number]] = {}
 
 
 def shared_range(flt_type, int_type):
diff --git a/nibabel/cmdline/dicomfs.py b/nibabel/cmdline/dicomfs.py
index 8de1438544..85d7d8dcad 100644
--- a/nibabel/cmdline/dicomfs.py
+++ b/nibabel/cmdline/dicomfs.py
@@ -25,7 +25,7 @@ class dummy_fuse:
 
 
 try:
-    import fuse
+    import fuse  # type: ignore
 
     uid = os.getuid()
     gid = os.getgid()
diff --git a/nibabel/ecat.py b/nibabel/ecat.py
index de81d8bbe8..8b11e881a7 100644
--- a/nibabel/ecat.py
+++ b/nibabel/ecat.py
@@ -50,7 +50,7 @@
 
 from .arraywriters import make_array_writer
 from .fileslice import canonical_slicers, predict_shape, slice2outax
-from .spatialimages import SpatialImage
+from .spatialimages import SpatialHeader, SpatialImage
 from .volumeutils import array_from_file, make_dt_codes, native_code, swapped_code
 from .wrapstruct import WrapStruct
 
@@ -243,7 +243,7 @@
 patient_orient_neurological = [1, 3, 5, 7]
 
 
-class EcatHeader(WrapStruct):
+class EcatHeader(WrapStruct, SpatialHeader):
     """Class for basic Ecat PET header
 
     Sub-parts of standard Ecat File
diff --git a/nibabel/externals/netcdf.py b/nibabel/externals/netcdf.py
index 2fddcf03d9..b8d1244c0c 100644
--- a/nibabel/externals/netcdf.py
+++ b/nibabel/externals/netcdf.py
@@ -871,6 +871,7 @@ def __setattr__(self, attr, value):
             pass
         self.__dict__[attr] = value
 
+    @property
     def isrec(self):
         """Returns whether the variable has a record dimension or not.
 
@@ -881,8 +882,8 @@ def isrec(self):
 
         """
         return bool(self.data.shape) and not self._shape[0]
-    isrec = property(isrec)
 
+    @property
     def shape(self):
         """Returns the shape tuple of the data variable.
 
@@ -890,7 +891,6 @@ def shape(self):
         same manner of other numpy arrays.
         """
         return self.data.shape
-    shape = property(shape)
 
     def getValue(self):
         """
diff --git a/nibabel/filebasedimages.py b/nibabel/filebasedimages.py
index e37a698f2f..598a735d23 100644
--- a/nibabel/filebasedimages.py
+++ b/nibabel/filebasedimages.py
@@ -7,9 +7,11 @@
 #
 ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ##
 """Common interface for any image format--volume or surface, binary or xml."""
+from __future__ import annotations
 
 import io
 from copy import deepcopy
+from typing import Type
 from urllib import request
 
 from .fileholders import FileHolder
@@ -74,7 +76,6 @@ class FileBasedImage:
 
     properties:
 
-       * shape
        * header
 
     methods:
@@ -118,25 +119,6 @@ class FileBasedImage:
 
        img.to_file_map()
 
-    You can get the data out again with::
-
-        img.get_fdata()
-
-    Less commonly, for some image types that support it, you might want to
-    fetch out the unscaled array via the object containing the data::
-
-        unscaled_data = img.dataoobj.get_unscaled()
-
-    Analyze-type images (including nifti) support this, but others may not
-    (MINC, for example).
-
-    Sometimes you might to avoid any loss of precision by making the
-    data type the same as the input::
-
-        hdr = img.header
-        hdr.set_data_dtype(data.dtype)
-        img.to_filename(fname)
-
     **Files interface**
 
     The image has an attribute ``file_map``.  This is a mapping, that has keys
@@ -158,20 +140,20 @@ class FileBasedImage:
     contain enough information so that an existing image instance can save
     itself back to the files pointed to in ``file_map``.  When a file holder
     holds active file-like objects, then these may be affected by the
-    initial file read; in this case, the contains file-like objects need to
+    initial file read; in this case, the file-like objects need to
     carry the position at which a write (with ``to_file_map``) should place the
     data.  The ``file_map`` contents should therefore be such, that this will
     work.
     """
 
-    header_class = FileBasedHeader
-    _meta_sniff_len = 0
-    files_types = (('image', None),)
-    valid_exts = ()
-    _compressed_suffixes = ()
+    header_class: Type[FileBasedHeader] = FileBasedHeader
+    _meta_sniff_len: int = 0
+    files_types: tuple[tuple[str, str | None], ...] = (('image', None),)
+    valid_exts: tuple[str, ...] = ()
+    _compressed_suffixes: tuple[str, ...] = ()
 
-    makeable = True  # Used in test code
-    rw = True  # Used in test code
+    makeable: bool = True  # Used in test code
+    rw: bool = True  # Used in test code
 
     def __init__(self, header=None, extra=None, file_map=None):
         """Initialize image
diff --git a/nibabel/freesurfer/mghformat.py b/nibabel/freesurfer/mghformat.py
index cb86b4400b..6b97056524 100644
--- a/nibabel/freesurfer/mghformat.py
+++ b/nibabel/freesurfer/mghformat.py
@@ -21,7 +21,7 @@
 from ..fileholders import FileHolder
 from ..filename_parser import _stringify_path
 from ..openers import ImageOpener
-from ..spatialimages import HeaderDataError, SpatialImage
+from ..spatialimages import HeaderDataError, SpatialHeader, SpatialImage
 from ..volumeutils import Recoder, array_from_file, array_to_file, endian_codes
 from ..wrapstruct import LabeledWrapStruct
 
@@ -87,7 +87,7 @@ class MGHError(Exception):
     """
 
 
-class MGHHeader(LabeledWrapStruct):
+class MGHHeader(LabeledWrapStruct, SpatialHeader):
     """Class for MGH format header
 
     The header also consists of the footer data which MGH places after the data
diff --git a/nibabel/gifti/gifti.py b/nibabel/gifti/gifti.py
index c80fbf2e22..919e4faef2 100644
--- a/nibabel/gifti/gifti.py
+++ b/nibabel/gifti/gifti.py
@@ -11,10 +11,12 @@
 The Gifti specification was (at time of writing) available as a PDF download
 from http://www.nitrc.org/projects/gifti/
 """
+from __future__ import annotations
 
 import base64
 import sys
 import warnings
+from typing import Type
 
 import numpy as np
 
@@ -577,7 +579,7 @@ class GiftiImage(xml.XmlSerializable, SerializableImage):
     # The parser will in due course be a GiftiImageParser, but we can't set
     # that now, because it would result in a circular import.  We set it after
     # the class has been defined, at the end of the class definition.
-    parser = None
+    parser: Type[xml.XmlParser]
 
     def __init__(
         self,
@@ -832,7 +834,7 @@ def _to_xml_element(self):
             GIFTI.append(dar._to_xml_element())
         return GIFTI
 
-    def to_xml(self, enc='utf-8'):
+    def to_xml(self, enc='utf-8') -> bytes:
         """Return XML corresponding to image content"""
         header = b"""<?xml version="1.0" encoding="UTF-8"?>
 <!DOCTYPE GIFTI SYSTEM "http://www.nitrc.org/frs/download.php/115/gifti.dtd">
@@ -840,9 +842,12 @@ def to_xml(self, enc='utf-8'):
         return header + super().to_xml(enc)
 
     # Avoid the indirection of going through to_file_map
-    to_bytes = to_xml
+    def to_bytes(self, enc='utf-8'):
+        return self.to_xml(enc=enc)
 
-    def to_file_map(self, file_map=None):
+    to_bytes.__doc__ = SerializableImage.to_bytes.__doc__
+
+    def to_file_map(self, file_map=None, enc='utf-8'):
         """Save the current image to the specified file_map
 
         Parameters
@@ -858,7 +863,7 @@ def to_file_map(self, file_map=None):
         if file_map is None:
             file_map = self.file_map
         with file_map['image'].get_prepare_fileobj('wb') as f:
-            f.write(self.to_xml())
+            f.write(self.to_xml(enc=enc))
 
     @classmethod
     def from_file_map(klass, file_map, buffer_size=35000000, mmap=True):
diff --git a/nibabel/minc1.py b/nibabel/minc1.py
index fb183277bc..b9d4bc2074 100644
--- a/nibabel/minc1.py
+++ b/nibabel/minc1.py
@@ -7,8 +7,10 @@
 #
 ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ##
 """Read MINC1 format images"""
+from __future__ import annotations
 
 from numbers import Integral
+from typing import Type
 
 import numpy as np
 
@@ -305,11 +307,11 @@ class Minc1Image(SpatialImage):
     load.
     """
 
-    header_class = Minc1Header
-    _meta_sniff_len = 4
-    valid_exts = ('.mnc',)
-    files_types = (('image', '.mnc'),)
-    _compressed_suffixes = ('.gz', '.bz2', '.zst')
+    header_class: Type[MincHeader] = Minc1Header
+    _meta_sniff_len: int = 4
+    valid_exts: tuple[str, ...] = ('.mnc',)
+    files_types: tuple[tuple[str, str], ...] = (('image', '.mnc'),)
+    _compressed_suffixes: tuple[str, ...] = ('.gz', '.bz2', '.zst')
 
     makeable = True
     rw = False
diff --git a/nibabel/minc2.py b/nibabel/minc2.py
index 1fffae0c86..cdb567a996 100644
--- a/nibabel/minc2.py
+++ b/nibabel/minc2.py
@@ -155,7 +155,7 @@ class Minc2Image(Minc1Image):
     def from_file_map(klass, file_map, *, mmap=True, keep_file_open=None):
         # Import of h5py might take awhile for MPI-enabled builds
         # So we are importing it here "on demand"
-        import h5py
+        import h5py  # type: ignore
 
         holder = file_map['image']
         if holder.filename is None:
diff --git a/nibabel/nicom/dicomwrappers.py b/nibabel/nicom/dicomwrappers.py
index 7e6bea9009..572957f391 100755
--- a/nibabel/nicom/dicomwrappers.py
+++ b/nibabel/nicom/dicomwrappers.py
@@ -127,8 +127,6 @@ class Wrapper:
     is_multiframe = False
     b_matrix = None
     q_vector = None
-    b_value = None
-    b_vector = None
 
     def __init__(self, dcm_data):
         """Initialize wrapper
diff --git a/nibabel/nifti1.py b/nibabel/nifti1.py
index 61a6da3660..9bb88e844c 100644
--- a/nibabel/nifti1.py
+++ b/nibabel/nifti1.py
@@ -10,8 +10,11 @@
 
 NIfTI1 format defined at http://nifti.nimh.nih.gov/nifti-1/
 """
+from __future__ import annotations
+
 import warnings
 from io import BytesIO
+from typing import Type
 
 import numpy as np
 import numpy.linalg as npl
@@ -87,8 +90,8 @@
 # datatypes not in analyze format, with codes
 if have_binary128():
     # Only enable 128 bit floats if we really have IEEE binary 128 longdoubles
-    _float128t = np.longdouble
-    _complex256t = np.longcomplex
+    _float128t: Type[np.generic] = np.longdouble
+    _complex256t: Type[np.generic] = np.longcomplex
 else:
     _float128t = np.void
     _complex256t = np.void
@@ -1814,7 +1817,7 @@ class Nifti1PairHeader(Nifti1Header):
 class Nifti1Pair(analyze.AnalyzeImage):
     """Class for NIfTI1 format image, header pair"""
 
-    header_class = Nifti1PairHeader
+    header_class: Type[Nifti1Header] = Nifti1PairHeader
     _meta_sniff_len = header_class.sizeof_hdr
     rw = True
 
@@ -1848,9 +1851,7 @@ def __init__(self, dataobj, affine, header=None, extra=None, file_map=None, dtyp
             self._affine2header()
 
     # Copy docstring
-    __init__.__doc__ = (
-        analyze.AnalyzeImage.__init__.__doc__
-        + """
+    __init__.__doc__ = f"""{analyze.AnalyzeImage.__init__.__doc__}
         Notes
         -----
 
@@ -1863,7 +1864,6 @@ def __init__(self, dataobj, affine, header=None, extra=None, file_map=None, dtyp
         :meth:`set_qform` methods can be used to update the codes after an image
         has been created - see those methods, and the :ref:`manual
         <default-sform-qform-codes>` for more details.  """
-    )
 
     def update_header(self):
         """Harmonize header with image data and affine
diff --git a/nibabel/openers.py b/nibabel/openers.py
index 4a1b911c95..d75839fe1a 100644
--- a/nibabel/openers.py
+++ b/nibabel/openers.py
@@ -20,7 +20,7 @@
 
 # is indexed_gzip present and modern?
 try:
-    import indexed_gzip as igzip
+    import indexed_gzip as igzip  # type: ignore
 
     version = igzip.__version__
 
diff --git a/nibabel/parrec.py b/nibabel/parrec.py
index 27ade56ae9..7c594dcb45 100644
--- a/nibabel/parrec.py
+++ b/nibabel/parrec.py
@@ -1338,7 +1338,7 @@ def from_filename(
             strict_sort=strict_sort,
         )
 
-    load = from_filename
+    load = from_filename  # type: ignore
 
 
-load = PARRECImage.load
+load = PARRECImage.from_filename
diff --git a/nibabel/pkg_info.py b/nibabel/pkg_info.py
index 068600b4e6..73dfd92ed2 100644
--- a/nibabel/pkg_info.py
+++ b/nibabel/pkg_info.py
@@ -70,7 +70,7 @@ def cmp_pkg_version(version_str: str, pkg_version_str: str = __version__) -> int
     return _cmp(Version(version_str), Version(pkg_version_str))
 
 
-def pkg_commit_hash(pkg_path: str = None) -> tuple[str, str]:
+def pkg_commit_hash(pkg_path: str | None = None) -> tuple[str, str]:
     """Get short form of commit hash
 
     In this file is a variable called COMMIT_HASH. This contains a substitution
@@ -109,7 +109,7 @@ def pkg_commit_hash(pkg_path: str = None) -> tuple[str, str]:
         cwd=pkg_path,
     )
     if proc.stdout:
-        return 'repository', proc.stdout.strip()
+        return 'repository', proc.stdout.decode().strip()
     return '(none found)', '<not found>'
 
 
diff --git a/nibabel/pydicom_compat.py b/nibabel/pydicom_compat.py
index 9ee2553c5a..4d9df7df7b 100644
--- a/nibabel/pydicom_compat.py
+++ b/nibabel/pydicom_compat.py
@@ -7,7 +7,7 @@
 without error, and always defines:
 
 * have_dicom : True if we can import pydicom or dicom;
-* pydicom : pydicom module or dicom module or None of not importable;
+* pydicom : pydicom module or dicom module or None if not importable;
 * read_file : ``read_file`` function if pydicom or dicom module is importable
   else None;
 * tag_for_keyword : ``tag_for_keyword`` function if pydicom or dicom module
@@ -19,26 +19,25 @@
 
 A deprecated copy is available here for backward compatibility.
 """
+from __future__ import annotations
 
-# Module has (apparently) unused imports; stop flake8 complaining
-# flake8: noqa
+from typing import Callable
 
 from .deprecated import deprecate_with_version
+from .optpkg import optional_package
 
-have_dicom = True
-pydicom = read_file = tag_for_keyword = Sequence = None
+pydicom, have_dicom, _ = optional_package('pydicom')
 
-try:
-    import pydicom
-except ImportError:
-    have_dicom = False
-else:  # pydicom module available
-    # Values not imported by default
-    import pydicom.values
-    from pydicom.dicomio import read_file
-    from pydicom.sequence import Sequence
+read_file: Callable | None = None
+tag_for_keyword: Callable | None = None
+Sequence: type | None = None
 
 if have_dicom:
+    # Values not imported by default
+    import pydicom.values  # type: ignore
+    from pydicom.dicomio import read_file  # noqa:F401
+    from pydicom.sequence import Sequence  # noqa:F401
+
     tag_for_keyword = pydicom.datadict.tag_for_keyword
 
 
diff --git a/nibabel/spatialimages.py b/nibabel/spatialimages.py
index 794bb750e6..4bd25e986f 100644
--- a/nibabel/spatialimages.py
+++ b/nibabel/spatialimages.py
@@ -129,6 +129,9 @@
     >>> np.all(img3.get_fdata(dtype=np.float32) == data)
     True
 """
+from __future__ import annotations
+
+from typing import Type
 
 import numpy as np
 
@@ -400,7 +403,7 @@ def slice_affine(self, slicer):
 class SpatialImage(DataobjImage):
     """Template class for volumetric (3D/4D) images"""
 
-    header_class = SpatialHeader
+    header_class: Type[SpatialHeader] = SpatialHeader
     ImageSlicer = SpatialFirstSlicer
 
     def __init__(self, dataobj, affine, header=None, extra=None, file_map=None):
diff --git a/nibabel/spm99analyze.py b/nibabel/spm99analyze.py
index 12e3cb658d..a089bedb02 100644
--- a/nibabel/spm99analyze.py
+++ b/nibabel/spm99analyze.py
@@ -274,7 +274,7 @@ def from_file_map(klass, file_map, *, mmap=True, keep_file_open=None):
             contents = matf.read()
         if len(contents) == 0:
             return ret
-        import scipy.io as sio
+        import scipy.io as sio  # type: ignore
 
         mats = sio.loadmat(BytesIO(contents))
         if 'mat' in mats:  # this overrides a 'M', and includes any flip
diff --git a/nibabel/testing/np_features.py b/nibabel/testing/np_features.py
index c0739a8502..eeb783900a 100644
--- a/nibabel/testing/np_features.py
+++ b/nibabel/testing/np_features.py
@@ -1,24 +1,16 @@
 """Look for changes in numpy behavior over versions
 """
+from functools import lru_cache
 
 import numpy as np
 
 
-def memmap_after_ufunc():
+@lru_cache(maxsize=None)
+def memmap_after_ufunc() -> bool:
     """Return True if ufuncs on memmap arrays always return memmap arrays
 
     This should be True for numpy < 1.12, False otherwise.
-
-    Memoize after first call.  We do this to avoid having to call this when
-    importing nibabel.testing, because we cannot depend on the source file
-    being present - see gh-571.
     """
-    if memmap_after_ufunc.result is not None:
-        return memmap_after_ufunc.result
     with open(__file__, 'rb') as fobj:
         mm_arr = np.memmap(fobj, mode='r', shape=(10,), dtype=np.uint8)
-        memmap_after_ufunc.result = isinstance(mm_arr + 1, np.memmap)
-    return memmap_after_ufunc.result
-
-
-memmap_after_ufunc.result = None
+        return isinstance(mm_arr + 1, np.memmap)
diff --git a/nibabel/tmpdirs.py b/nibabel/tmpdirs.py
index 5a8eccfa2c..a3be77ffa8 100644
--- a/nibabel/tmpdirs.py
+++ b/nibabel/tmpdirs.py
@@ -16,7 +16,7 @@
     from contextlib import chdir as _chdir
 except ImportError:  # PY310
 
-    @contextmanager
+    @contextmanager  # type: ignore
     def _chdir(path):
         cwd = os.getcwd()
         os.chdir(path)
diff --git a/nibabel/volumeutils.py b/nibabel/volumeutils.py
index b339b6bab5..225062b2cb 100644
--- a/nibabel/volumeutils.py
+++ b/nibabel/volumeutils.py
@@ -7,6 +7,7 @@
 #
 ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ### ##
 """Utility functions for analyze-like formats"""
+from __future__ import annotations
 
 import gzip
 import sys
@@ -29,7 +30,7 @@
 native_code = sys_is_le and '<' or '>'
 swapped_code = sys_is_le and '>' or '<'
 
-endian_codes = (  # numpy code, aliases
+_endian_codes = (  # numpy code, aliases
     ('<', 'little', 'l', 'le', 'L', 'LE'),
     ('>', 'big', 'BIG', 'b', 'be', 'B', 'BE'),
     (native_code, 'native', 'n', 'N', '=', '|', 'i', 'I'),
@@ -41,7 +42,7 @@
 default_compresslevel = 1
 
 #: file-like classes known to hold compressed data
-COMPRESSED_FILE_LIKES = (gzip.GzipFile, BZ2File, IndexedGzipFile)
+COMPRESSED_FILE_LIKES: tuple[type, ...] = (gzip.GzipFile, BZ2File, IndexedGzipFile)
 
 # Enable .zst support if pyzstd installed.
 if HAVE_ZSTD:
@@ -220,7 +221,7 @@ def value_set(self, name=None):
 
 
 # Endian code aliases
-endian_codes = Recoder(endian_codes)
+endian_codes = Recoder(_endian_codes)
 
 
 class DtypeMapper:
diff --git a/nibabel/wrapstruct.py b/nibabel/wrapstruct.py
index bf29e0828a..6e236d7356 100644
--- a/nibabel/wrapstruct.py
+++ b/nibabel/wrapstruct.py
@@ -109,11 +109,13 @@
 
    nib.imageglobals.logger = logger
 """
+from __future__ import annotations
+
 import numpy as np
 
 from . import imageglobals as imageglobals
 from .batteryrunners import BatteryRunner
-from .volumeutils import endian_codes, native_code, pretty_mapping, swapped_code
+from .volumeutils import Recoder, endian_codes, native_code, pretty_mapping, swapped_code
 
 
 class WrapStructError(Exception):
@@ -482,7 +484,7 @@ def _get_checks(klass):
 class LabeledWrapStruct(WrapStruct):
     """A WrapStruct with some fields having value labels for printing etc"""
 
-    _field_recoders = {}  # for recoding values for str
+    _field_recoders: dict[str, Recoder] = {}  # for recoding values for str
 
     def get_value_label(self, fieldname):
         """Returns label for coded field
diff --git a/pyproject.toml b/pyproject.toml
index 5a1162a5a6..6d44c607ed 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -68,6 +68,7 @@ test = [
   "pytest-httpserver",
   "pytest-xdist",
 ]
+typing = ["mypy", "pytest", "types-setuptools", "types-Pillow", "pydicom"]
 zstd = ["pyzstd >= 0.14.3"]
 
 [tool.hatch.build.targets.sdist]
@@ -102,3 +103,9 @@ force-exclude = """
 profile = "black"
 line_length = 99
 extend_skip = ["_version.py", "externals"]
+
+[tool.mypy]
+python_version = "3.11"
+exclude = [
+  "/tests",
+]
diff --git a/tools/ci/check.sh b/tools/ci/check.sh
index 3cfc1e5530..bcb1a934e2 100755
--- a/tools/ci/check.sh
+++ b/tools/ci/check.sh
@@ -25,6 +25,8 @@ elif [ "${CHECK_TYPE}" == "test" ]; then
     cp ../.coveragerc .
     pytest --doctest-modules --doctest-plus --cov nibabel --cov-report xml \
         --junitxml=test-results.xml -v --pyargs nibabel -n auto
+elif [ "${CHECK_TYPE}" == "typing" ]; then
+    mypy nibabel
 else
     false
 fi