diff --git a/.pre-commit-config.yaml b/.pre-commit-config.yaml
index 8d13fe15..792d8185 100644
--- a/.pre-commit-config.yaml
+++ b/.pre-commit-config.yaml
@@ -12,7 +12,7 @@ repos:
   - id: mixed-line-ending
   - id: trailing-whitespace
 
-- repo: https://github.com/psf/black
+- repo: https://github.com/psf/black-pre-commit-mirror
   rev: 23.9.1
   hooks:
   - id: black
@@ -54,3 +54,14 @@ repos:
   - id: blacken-docs
     additional_dependencies:
     - black
+
+- repo: https://github.com/pre-commit/mirrors-mypy
+  rev: v1.6.0
+  hooks:
+  - id: mypy
+    args: [--ignore-missing-imports]
+    additional_dependencies:
+    - dask
+    - types-PyYAML
+    - pytest
+    - numpy
diff --git a/docs/dev/contributing.rst b/docs/dev/contributing.rst
index bd89514d..90cecc5e 100644
--- a/docs/dev/contributing.rst
+++ b/docs/dev/contributing.rst
@@ -34,6 +34,14 @@ Commit your changes, push your branch to your fork, and open a Pull
 Request. We suggest that you install `pre-commit <precommit_>`_ to run
 some checks locally when creating new commits.
 
+Typing
+------
+
+We include a pre-commit hook that runs ``mypy`` for static type
+checking. Code added to dask-awkward is *not required* to be typed,
+but the pre-commit check does enforce correctness when type hints are
+present.
+
 Adding documentation
 --------------------
 
diff --git a/pyproject.toml b/pyproject.toml
index 35bf16cf..e063c033 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -109,6 +109,7 @@ src_paths = ["src", "tests"]
 [tool.mypy]
 python_version = "3.9"
 files = ["src", "tests"]
+strict = false
 warn_unused_configs = true
 show_error_codes = true
 allow_incomplete_defs = false
diff --git a/src/dask_awkward/layers/layers.py b/src/dask_awkward/layers/layers.py
index 747ff80b..4bbcfc14 100644
--- a/src/dask_awkward/layers/layers.py
+++ b/src/dask_awkward/layers/layers.py
@@ -44,7 +44,7 @@ def __repr__(self) -> str:
 
 
 class ImplementsIOFunction(Protocol):
-    def __call__(self, *args, **kwargs) -> AwkwardArray:
+    def __call__(self, *args: Any, **kwargs: Any) -> AwkwardArray:
         ...
 
 
@@ -79,7 +79,7 @@ def __getstate__(self) -> dict:
         state["_meta"] = None
         return state
 
-    def __call__(self, *args, **kwargs) -> AwkwardArray:
+    def __call__(self, *args, **kwargs):
         return self._io_func(*args, **kwargs)
 
     def mock(self) -> AwkwardArray:
@@ -220,7 +220,7 @@ def project(
         self,
         report: TypeTracerReport,
         state: T,
-    ):
+    ) -> AwkwardInputLayer:
         assert self.is_projectable
         return AwkwardInputLayer(
             name=self.name,
diff --git a/src/dask_awkward/lib/core.py b/src/dask_awkward/lib/core.py
index 93fcbf7d..d8450d97 100644
--- a/src/dask_awkward/lib/core.py
+++ b/src/dask_awkward/lib/core.py
@@ -42,7 +42,6 @@
 
 from dask_awkward.layers import AwkwardBlockwiseLayer, AwkwardMaterializedLayer
 from dask_awkward.lib.optimize import all_optimizations
-from dask_awkward.typing import AwkwardDaskCollection
 from dask_awkward.utils import (
     DaskAwkwardNotImplemented,
     IncompatiblePartitions,
@@ -370,7 +369,7 @@ def _check_meta(self, m: Any | None) -> Any | None:
             raise TypeError(f"meta must be a Record typetracer object, not a {type(m)}")
         return m
 
-    def __getitem__(self, where: str) -> AwkwardDaskCollection:
+    def __getitem__(self, where):
         token = tokenize(self, where)
         new_name = f"{where}-{token}"
         new_meta = self._meta[where]
@@ -397,7 +396,7 @@ def __getitem__(self, where: str) -> AwkwardDaskCollection:
         else:
             return new_scalar_object(hlg, new_name, meta=new_meta)
 
-    def __getattr__(self, attr: str) -> Any:
+    def __getattr__(self, attr):
         if attr not in (self.fields or []):
             raise AttributeError(f"{attr} not in fields.")
         try:
diff --git a/src/dask_awkward/lib/inspect.py b/src/dask_awkward/lib/inspect.py
index 030a5012..58635833 100644
--- a/src/dask_awkward/lib/inspect.py
+++ b/src/dask_awkward/lib/inspect.py
@@ -23,6 +23,7 @@ def report_necessary_buffers(
     *args: Any, traverse: bool = True
 ) -> dict[str, NecessaryBuffers | None]:
     r"""Determine the buffer keys necessary to compute a collection.
+
     Parameters
     ----------
     *args : Dask collections or HighLevelGraphs
@@ -31,24 +32,30 @@ def report_necessary_buffers(
     traverse : bool, optional
         If True (default), builtin Python collections are traversed
         looking for any Dask collections they might contain.
+
     Returns
     -------
     dict[str, NecessaryBuffers | None]
         Mapping that pairs the input layers in the graph to objects
         describing the data and shape buffers that have been tagged
         as required by column optimisation of the given layer.
+
     Examples
     --------
     If we have a hypothetical parquet dataset (``ds``) with the fields
+
     - "foo"
     - "bar"
     - "baz"
+
     And the "baz" field has fields
 
     - "x"
     - "y"
+
     The calculation of ``ds.bar + ds.baz.x`` will only require the
     ``bar`` and ``baz.x`` columns from the parquet file.
+
     >>> import dask_awkward as dak
     >>> ds = dak.from_parquet("some-dataset")
     >>> ds.fields
@@ -96,6 +103,7 @@ def report_necessary_buffers(
             shape_only = frozenset(report.shape_touched) - data_and_shape
 
             # Update set of touched keys
+            assert existing_buffers is not None
             name_to_necessary_buffers[name] = NecessaryBuffers(
                 data_and_shape=existing_buffers.data_and_shape | data_and_shape,
                 shape_only=existing_buffers.shape_only | shape_only,
@@ -161,7 +169,7 @@ def report_necessary_columns(
 
     seen_names = set()
 
-    name_to_necessary_columns: dict[str, frozenset] = {}
+    name_to_necessary_columns: dict[str, frozenset | None] = {}
     for obj in collections:
         dsk = obj if isinstance(obj, HighLevelGraph) else obj.dask
         projection_data = o._prepare_buffer_projection(dsk)
@@ -183,6 +191,7 @@ def report_necessary_columns(
 
             existing_columns = name_to_necessary_columns.setdefault(name, frozenset())
 
+            assert existing_columns is not None
             # Update set of touched keys
             name_to_necessary_columns[
                 name
@@ -237,11 +246,14 @@ def sample(
         rows will remain.
 
     """
-    if not (factor is None) ^ (probability is None):
+    if (factor is None and probability is None) or (
+        factor is not None and probability is not None
+    ):
         raise ValueError("Give exactly one of factor or probability")
     if factor:
         return arr.map_partitions(lambda x: x[::factor], meta=arr._meta)
-    else:
-        return arr.map_partitions(
-            lambda x: x[_random_boolean_like(x, probability)], meta=arr._meta
-        )
+    assert probability is not None
+    proba = float(probability)
+    return arr.map_partitions(
+        lambda x: x[_random_boolean_like(x, proba)], meta=arr._meta
+    )
diff --git a/src/dask_awkward/lib/io/columnar.py b/src/dask_awkward/lib/io/columnar.py
index 88b8bb02..fed93f1f 100644
--- a/src/dask_awkward/lib/io/columnar.py
+++ b/src/dask_awkward/lib/io/columnar.py
@@ -1,13 +1,13 @@
 from __future__ import annotations
 
 import logging
-from typing import TYPE_CHECKING, Protocol, TypeVar, cast
+from typing import TYPE_CHECKING, Any, Protocol, TypeVar, cast
 
 import awkward as ak
 from awkward import Array as AwkwardArray
 from awkward.forms import Form
 
-from dask_awkward.layers.layers import ImplementsNecessaryColumns
+from dask_awkward.layers.layers import ImplementsIOFunction, ImplementsNecessaryColumns
 from dask_awkward.lib.utils import (
     METADATA_ATTRIBUTES,
     FormStructure,
@@ -39,6 +39,9 @@ def behavior(self) -> dict | None:
     def project_columns(self: T, columns: frozenset[str]) -> T:
         ...
 
+    def __call__(self, *args: Any, **kwargs: Any) -> AwkwardArray:
+        ...
+
 
 S = TypeVar("S", bound=ImplementsColumnProjectionMixin)
 
@@ -84,7 +87,7 @@ def necessary_columns(
         form_key_to_parent_form_key = state["form_key_to_parent_form_key"]
         form_key_to_child_form_keys: dict[str, list[str]] = {}
         for child_key, parent_key in form_key_to_parent_form_key.items():
-            form_key_to_child_form_keys.setdefault(parent_key, []).append(child_key)
+            form_key_to_child_form_keys.setdefault(parent_key, []).append(child_key)  # type: ignore
         form_key_to_form = state["form_key_to_form"]
         # Buffer hierarchy information
         form_key_to_buffer_keys = state["form_key_to_buffer_keys"]
@@ -151,8 +154,8 @@ def project(
         self: S,
         report: TypeTracerReport,
         state: FormStructure,
-    ) -> S:
-        if not self.use_optimization:
+    ) -> ImplementsIOFunction:
+        if not self.use_optimization:  # type: ignore[attr-defined]
             return self
 
         return self.project_columns(self.necessary_columns(report, state))
diff --git a/src/dask_awkward/lib/io/io.py b/src/dask_awkward/lib/io/io.py
index b1cd51fb..9166b9a0 100644
--- a/src/dask_awkward/lib/io/io.py
+++ b/src/dask_awkward/lib/io/io.py
@@ -4,7 +4,7 @@
 import warnings
 from collections.abc import Iterable
 from dataclasses import dataclass
-from typing import TYPE_CHECKING, Any, Callable, Mapping, Protocol, cast
+from typing import TYPE_CHECKING, Any, Callable, cast
 
 import awkward as ak
 import numpy as np
diff --git a/src/dask_awkward/lib/io/json.py b/src/dask_awkward/lib/io/json.py
index fcb0a9ec..bf7d96e6 100644
--- a/src/dask_awkward/lib/io/json.py
+++ b/src/dask_awkward/lib/io/json.py
@@ -67,7 +67,7 @@ def use_optimization(self) -> bool:
             and self.schema is None
         )
 
-    def project_columns(self, columns: set[str]):
+    def project_columns(self, columns):
         form = self.form.select_columns(columns)
         assert form is not None
         schema = layout_to_jsonschema(form.length_zero_array(highlevel=False))
diff --git a/src/dask_awkward/lib/io/parquet.py b/src/dask_awkward/lib/io/parquet.py
index df03e42c..a18a90c1 100644
--- a/src/dask_awkward/lib/io/parquet.py
+++ b/src/dask_awkward/lib/io/parquet.py
@@ -59,7 +59,7 @@ def __call__(self, source: Any) -> ak.Array:
         ...
 
     @abc.abstractmethod
-    def project_columns(self, columns: set[str]):
+    def project_columns(self, columns):
         ...
 
     @property
@@ -122,7 +122,7 @@ def __call__(self, source: Any) -> Any:
         )
         return ak.Array(unproject_layout(self.original_form, array.layout))
 
-    def project_columns(self, columns: set[str]):
+    def project_columns(self, columns):
         return _FromParquetFileWiseFn(
             fs=self.fs,
             form=self.form.select_columns(columns),
@@ -172,7 +172,7 @@ def __call__(self, pair: Any) -> ak.Array:
         )
         return ak.Array(unproject_layout(self.original_form, array.layout))
 
-    def project_columns(self, columns: set[str]):
+    def project_columns(self, columns):
         return _FromParquetFragmentWiseFn(
             fs=self.fs,
             form=self.form.select_columns(columns),
diff --git a/src/dask_awkward/lib/optimize.py b/src/dask_awkward/lib/optimize.py
index 24656899..599f234a 100644
--- a/src/dask_awkward/lib/optimize.py
+++ b/src/dask_awkward/lib/optimize.py
@@ -431,5 +431,5 @@ def _recursive_replace(args, layer, parent, indices):
 
 def _buffer_keys_for_layer(
     buffer_keys: Iterable[str], known_buffer_keys: frozenset[str]
-):
+) -> set[str]:
     return {k for k in buffer_keys if k in known_buffer_keys}
diff --git a/src/dask_awkward/lib/utils.py b/src/dask_awkward/lib/utils.py
index 2448dfb9..a25b3dd5 100644
--- a/src/dask_awkward/lib/utils.py
+++ b/src/dask_awkward/lib/utils.py
@@ -2,7 +2,7 @@
 
 __all__ = ("trace_form_structure", "buffer_keys_required_to_compute_shapes")
 
-from collections.abc import Callable, Iterable, Iterator
+from collections.abc import Callable, Iterable, Iterator, Mapping, MutableMapping
 from typing import TYPE_CHECKING, TypedDict, TypeVar
 
 import awkward as ak
@@ -17,19 +17,23 @@
 
 
 class FormStructure(TypedDict):
-    form_key_to_form: dict[str, Form]
-    form_key_to_parent_form_key: dict[str, str]
-    form_key_to_path: dict[str, tuple[str, ...]]
-    form_key_to_buffer_keys: dict[str, tuple[str, ...]]
+    form_key_to_form: MutableMapping[str, Form]
+    form_key_to_parent_form_key: MutableMapping[str, str | None]
+    form_key_to_path: MutableMapping[str, tuple[str, ...]]
+    form_key_to_buffer_keys: MutableMapping[str, tuple[str, ...]]
 
 
 def trace_form_structure(form: Form, buffer_key: Callable) -> FormStructure:
-    form_key_to_form: dict[str, Form] = {}
-    form_key_to_parent_form_key: dict[str, str | None] = {}
-    form_key_to_path: dict[str, tuple[str, ...]] = {}
-    form_key_to_buffer_keys: dict[str, tuple[str, ...]] = {}
-
-    def impl_with_parent(form: Form, parent_form: Form | None, column_path):
+    form_key_to_form: MutableMapping[str, Form] = {}
+    form_key_to_parent_form_key: MutableMapping[str, str | None] = {}
+    form_key_to_path: MutableMapping[str, tuple[str, ...]] = {}
+    form_key_to_buffer_keys: MutableMapping[str, tuple[str, ...]] = {}
+
+    def impl_with_parent(
+        form: Form,
+        parent_form: Form | None,
+        column_path: tuple[str, ...],
+    ) -> None:
         # Associate child form key with parent form key
         form_key_to_parent_form_key[form.form_key] = (
             None if parent_form is None else parent_form.form_key
@@ -74,13 +78,13 @@ def impl_with_parent(form: Form, parent_form: Form | None, column_path):
 T = TypeVar("T")
 
 
-def walk_bijective_graph(node: T, graph: dict[T, T | None]) -> Iterator[T]:
-    while (node := graph.get(node)) is not None:
+def walk_bijective_graph(node: T, graph: Mapping[T, T | None]) -> Iterator[T]:
+    while (node := graph.get(node)) is not None:  # type: ignore[assignment]
         yield node
 
 
 def walk_graph_breadth_first(
-    node: T, graph: dict[T, Iterable[T] | None]
+    node: T, graph: Mapping[T, Iterable[T] | None]
 ) -> Iterator[T]:
     children = graph.get(node)
     if children is None:
@@ -90,7 +94,9 @@ def walk_graph_breadth_first(
         yield from walk_graph_breadth_first(node, graph)
 
 
-def walk_graph_depth_first(node: T, graph: dict[T, Iterable[T] | None]) -> Iterator[T]:
+def walk_graph_depth_first(
+    node: T, graph: Mapping[T, Iterable[T] | None]
+) -> Iterator[T]:
     children = graph.get(node)
     if children is None:
         return
@@ -102,9 +108,9 @@ def walk_graph_depth_first(node: T, graph: dict[T, Iterable[T] | None]) -> Itera
 def buffer_keys_required_to_compute_shapes(
     parse_buffer_key: Callable[[str], tuple[str, str]],
     shape_buffers: Iterable[str],
-    form_key_to_parent_key: dict[str, str],
-    form_key_to_buffer_keys: dict[str, Iterable[str]],
-):
+    form_key_to_parent_key: Mapping[str, str | None],
+    form_key_to_buffer_keys: Mapping[str, Iterable[str]],
+) -> Iterable[str]:
     # Buffers needing known shapes must traverse all the way up the tree.
     for buffer_key in shape_buffers:
         form_key, attribute = parse_buffer_key(buffer_key)
@@ -126,11 +132,12 @@ def render_buffer_key(form: Form, form_key: str, attribute: str) -> str:
 
 
 def parse_buffer_key(buffer_key: str) -> tuple[str, str]:
-    return buffer_key.rsplit("-", maxsplit=1)
+    head, tail = buffer_key.rsplit("-", maxsplit=1)
+    return head, tail
 
 
 def form_with_unique_keys(form: Form, key: str) -> Form:
-    def impl(form: Form, key: str):
+    def impl(form: Form, key: str) -> None:
         # Set form key
         form.form_key = key
 
diff --git a/tests/conftest.py b/tests/conftest.py
index 09d629cd..c1c5fc38 100644
--- a/tests/conftest.py
+++ b/tests/conftest.py
@@ -1,9 +1,6 @@
 from __future__ import annotations
 
-try:
-    import ujson as json
-except ImportError:
-    import json  # type: ignore[no-redef]
+import json
 
 import awkward as ak
 import fsspec
diff --git a/tests/test_core.py b/tests/test_core.py
index c3924e7d..e23766f1 100644
--- a/tests/test_core.py
+++ b/tests/test_core.py
@@ -1,6 +1,8 @@
 from __future__ import annotations
 
 import copy
+import json
+import sys
 from collections import namedtuple
 from collections.abc import Callable
 from typing import TYPE_CHECKING
@@ -12,13 +14,6 @@
 import numpy as np
 import pytest
 
-try:
-    import ujson as json
-except ImportError:
-    import json  # type: ignore[no-redef]
-
-import sys
-
 import dask_awkward as dak
 from dask_awkward.lib.core import (
     Record,
diff --git a/tests/test_io_json.py b/tests/test_io_json.py
index 578358ef..15bb14d2 100644
--- a/tests/test_io_json.py
+++ b/tests/test_io_json.py
@@ -1,5 +1,6 @@
 from __future__ import annotations
 
+import json
 import os
 from pathlib import Path
 
@@ -13,12 +14,6 @@
 from dask_awkward.lib.optimize import optimize as dak_optimize
 from dask_awkward.lib.testutils import assert_eq
 
-try:
-    import ujson as json
-except ImportError:
-    import json  # type: ignore[no-redef]
-
-
 data1 = r"""{"name":"Bob","team":"tigers","goals":[0,0,0,1,2,0,1]}
 {"name":"Alice","team":"bears","goals":[null]}
 {"name":"Jack","team":"bears","goals":[0,0,0,0,0,0,0,0,1]}
@@ -85,7 +80,7 @@ def input_layer_array_partition0(collection: Array) -> ak.Array:
     """
     with dask.config.set({"awkward.optimization.which": ["columns"]}):
         optimized_hlg = dak_optimize(collection.dask, [])
-        layers = list(optimized_hlg.layers)  # type: ignore[attr-defined]
+        layers = list(optimized_hlg.layers)  # type: ignore
         layer_name = [name for name in layers if name.startswith("from-json")][0]
         sgc, arg = optimized_hlg[(layer_name, 0)]
         array = sgc.dsk[layer_name][0](arg)