diff --git a/.github/workflows/ci.yaml b/.github/workflows/ci.yaml
index 72bec4a4..a2992dae 100644
--- a/.github/workflows/ci.yaml
+++ b/.github/workflows/ci.yaml
@@ -23,9 +23,15 @@ jobs:
           python-version: ${{ matrix.python-version }}
           cache: "pip"
       - name: Install dependencies
-        run: python -m pip install -r requirements.txt -r requirements-dev.txt .
+        run: |
+          python -m pip install -r requirements.txt -r requirements-dev.txt .
+          yes | python -m mypy --install-types replicate || true
+
       - name: Lint
-        run: python -m ruff .
+        run: |
+          python -m mypy replicate
+          python -m ruff .
+          python -m black --check .
       - name: Test
         run: python -m pytest
 
diff --git a/pyproject.toml b/pyproject.toml
index 24400d23..46518389 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -11,7 +11,13 @@ license = { file = "LICENSE" }
 authors = [{ name = "Replicate, Inc." }]
 requires-python = ">=3.8"
 dependencies = ["packaging", "pydantic>1", "requests>2"]
-optional-dependencies = { dev = ["black", "pytest", "responses", "ruff"] }
+optional-dependencies = { dev = [
+    "black",
+    "mypy",
+    "pytest",
+    "responses",
+    "ruff",
+] }
 
 [project.urls]
 homepage = "https://replicate.com"
@@ -31,11 +37,21 @@ select = [
     "BLE", # flake8-blind-except
     "FBT", # flake8-boolean-trap
     "B",   # flake8-bugbear
+    "ANN", # flake8-annotations
 ]
 ignore = [
-    "E501", # Line too long
-    "S113", # Probable use of requests call without timeout
+    "E501",   # Line too long
+    "S113",   # Probable use of requests call without timeout
+    "ANN001", # Missing type annotation for function argument
+    "ANN002", # Missing type annotation for `*args`
+    "ANN003", # Missing type annotation for `**kwargs`
+    "ANN101", # Missing type annotation for self in method
+    "ANN102", # Missing type annotation for cls in classmethod
 ]
 
 [tool.ruff.per-file-ignores]
-"tests/*" = ["S101", "S106"]
+"tests/*" = [
+    "S101",   # Use of assert
+    "S106",   # Possible use of hard-coded password function arguments
+    "ANN201", # Missing return type annotation for public function
+]
diff --git a/replicate/base_model.py b/replicate/base_model.py
index 164ca045..b3cf1d48 100644
--- a/replicate/base_model.py
+++ b/replicate/base_model.py
@@ -1,9 +1,10 @@
-from typing import ForwardRef
+from typing import TYPE_CHECKING
 
-import pydantic
+if TYPE_CHECKING:
+    from replicate.client import Client
+    from replicate.collection import Collection
 
-Client = ForwardRef("Client")
-Collection = ForwardRef("Collection")
+import pydantic
 
 
 class BaseModel(pydantic.BaseModel):
@@ -11,10 +12,12 @@ class BaseModel(pydantic.BaseModel):
     A base class for representing a single object on the server.
     """
 
-    _client: Client = pydantic.PrivateAttr()
-    _collection: Collection = pydantic.PrivateAttr()
+    id: str
+
+    _client: "Client" = pydantic.PrivateAttr()
+    _collection: "Collection" = pydantic.PrivateAttr()
 
-    def reload(self):
+    def reload(self) -> None:
         """
         Load this object from the server again.
         """
diff --git a/replicate/client.py b/replicate/client.py
index 75409787..4196d6aa 100644
--- a/replicate/client.py
+++ b/replicate/client.py
@@ -1,7 +1,7 @@
 import os
 import re
 from json import JSONDecodeError
-from typing import Any, Iterator, Union
+from typing import Any, Dict, Iterator, Optional, Union
 
 import requests
 from requests.adapters import HTTPAdapter, Retry
@@ -14,7 +14,7 @@
 
 
 class Client:
-    def __init__(self, api_token=None) -> None:
+    def __init__(self, api_token: Optional[str] = None) -> None:
         super().__init__()
         # Client is instantiated at import time, so do as little as possible.
         # This includes resolving environment variables -- they might be set programmatically.
@@ -30,7 +30,7 @@ def __init__(self, api_token=None) -> None:
             total=5,
             backoff_factor=2,
             # Only retry 500s on GET so we don't unintionally mutute data
-            method_whitelist=["GET"],
+            allowed_methods=["GET"],
             # https://support.cloudflare.com/hc/en-us/articles/115003011431-Troubleshooting-Cloudflare-5XX-errors
             status_forcelist=[
                 429,
@@ -54,14 +54,14 @@ def __init__(self, api_token=None) -> None:
         write_retries = Retry(
             total=5,
             backoff_factor=2,
-            method_whitelist=["POST", "PUT"],
+            allowed_methods=["POST", "PUT"],
             # Only retry POST/PUT requests on rate limits, so we don't unintionally mutute data
             status_forcelist=[429],
         )
         self.write_session.mount("http://", HTTPAdapter(max_retries=write_retries))
         self.write_session.mount("https://", HTTPAdapter(max_retries=write_retries))
 
-    def _request(self, method: str, path: str, **kwargs):
+    def _request(self, method: str, path: str, **kwargs) -> requests.Response:
         # from requests.Session
         if method in ["GET", "OPTIONS"]:
             kwargs.setdefault("allow_redirects", True)
@@ -81,13 +81,13 @@ def _request(self, method: str, path: str, **kwargs):
             raise ReplicateError(f"HTTP error: {resp.status_code, resp.reason}")
         return resp
 
-    def _headers(self):
+    def _headers(self) -> Dict[str, str]:
         return {
             "Authorization": f"Token {self._api_token()}",
             "User-Agent": f"replicate-python@{__version__}",
         }
 
-    def _api_token(self):
+    def _api_token(self) -> str:
         token = self.api_token
         # Evaluate lazily in case environment variable is set with dotenv, or something
         if token is None:
@@ -112,7 +112,7 @@ def predictions(self) -> PredictionCollection:
     def trainings(self) -> TrainingCollection:
         return TrainingCollection(client=self)
 
-    def run(self, model_version, **kwargs) -> Union[Any, Iterator[Any]]:
+    def run(self, model_version: str, **kwargs) -> Union[Any, Iterator[Any]]:
         """
         Run a model in the format owner/name:version.
         """
diff --git a/replicate/collection.py b/replicate/collection.py
index 94766aae..92e7a88a 100644
--- a/replicate/collection.py
+++ b/replicate/collection.py
@@ -1,38 +1,54 @@
+import abc
+from typing import TYPE_CHECKING, Dict, Generic, List, TypeVar, Union, cast
+
+if TYPE_CHECKING:
+    from replicate.client import Client
+
 from replicate.base_model import BaseModel
 
+Model = TypeVar("Model", bound=BaseModel)
+
 
-class Collection:
+class Collection(abc.ABC, Generic[Model]):
     """
     A base class for representing all objects of a particular type on the
     server.
     """
 
-    model: BaseModel = None
-
-    def __init__(self, client=None):
+    def __init__(self, client: "Client") -> None:
         self._client = client
 
-    def list(self):
-        raise NotImplementedError
+    @abc.abstractproperty
+    def model(self) -> Model:
+        pass
+
+    @abc.abstractmethod
+    def list(self) -> List[Model]:
+        pass
 
-    def get(self, key):
-        raise NotImplementedError
+    @abc.abstractmethod
+    def get(self, key: str) -> Model:
+        pass
 
-    def create(self, attrs=None):
-        raise NotImplementedError
+    @abc.abstractmethod
+    def create(self, **kwargs) -> Model:
+        pass
 
-    def prepare_model(self, attrs):
+    def prepare_model(self, attrs: Union[Model, Dict]) -> Model:
         """
         Create a model from a set of attributes.
         """
         if isinstance(attrs, BaseModel):
             attrs._client = self._client
             attrs._collection = self
-            return attrs
-        elif isinstance(attrs, dict):
+            return cast(Model, attrs)
+        elif (
+            isinstance(attrs, dict) and self.model is not None and callable(self.model)
+        ):
             model = self.model(**attrs)
             model._client = self._client
             model._collection = self
             return model
         else:
-            raise Exception(f"Can't create {self.model.__name__} from {attrs}")
+            name = self.model.__name__ if hasattr(self.model, "__name__") else "model"
+            raise Exception(f"Can't create {name} from {attrs}")
diff --git a/replicate/files.py b/replicate/files.py
index c93d411f..55a6612c 100644
--- a/replicate/files.py
+++ b/replicate/files.py
@@ -2,11 +2,12 @@
 import io
 import mimetypes
 import os
+from typing import Optional
 
 import requests
 
 
-def upload_file(fh: io.IOBase, output_file_prefix: str = None) -> str:
+def upload_file(fh: io.IOBase, output_file_prefix: Optional[str] = None) -> str:
     """
     Lifted straight from cog.files
     """
diff --git a/replicate/json.py b/replicate/json.py
index bab3b4d8..cd0b864e 100644
--- a/replicate/json.py
+++ b/replicate/json.py
@@ -11,7 +11,9 @@
     has_numpy = False
 
 
-def encode_json(obj: Any, upload_file: Callable[[io.IOBase], str]) -> Any:
+def encode_json(
+    obj: Any, upload_file: Callable[[io.IOBase], str]  # noqa: ANN401
+) -> Any:  # noqa: ANN401
     """
     Returns a JSON-compatible version of the object. Effectively the same thing as cog.json.encode_json.
     """
diff --git a/replicate/model.py b/replicate/model.py
index 5d240955..d6b32fcd 100644
--- a/replicate/model.py
+++ b/replicate/model.py
@@ -1,3 +1,5 @@
+from typing import Dict, List, Union
+
 from replicate.base_model import BaseModel
 from replicate.collection import Collection
 from replicate.exceptions import ReplicateException
@@ -8,21 +10,34 @@ class Model(BaseModel):
     username: str
     name: str
 
-    def predict(self, *args, **kwargs):
+    def predict(self, *args, **kwargs) -> None:
         raise ReplicateException(
             "The `model.predict()` method has been removed, because it's unstable: if a new version of the model you're using is pushed and its API has changed, your code may break. Use `version.predict()` instead. See https://github.com/replicate/replicate-python#readme"
         )
 
     @property
-    def versions(self):
+    def versions(self) -> VersionCollection:
         return VersionCollection(client=self._client, model=self)
 
 
 class ModelCollection(Collection):
     model = Model
 
+    def list(self) -> List[Model]:
+        raise NotImplementedError()
+
     def get(self, name: str) -> Model:
         # TODO: fetch model from server
         # TODO: support permanent IDs
         username, name = name.split("/")
         return self.prepare_model({"username": username, "name": name})
+
+    def create(self, **kwargs) -> Model:
+        raise NotImplementedError()
+
+    def prepare_model(self, attrs: Union[Model, Dict]) -> Model:
+        if isinstance(attrs, BaseModel):
+            attrs.id = f"{attrs.username}/{attrs.name}"
+        elif isinstance(attrs, dict):
+            attrs["id"] = f"{attrs['username']}/{attrs['name']}"
+        return super().prepare_model(attrs)
diff --git a/replicate/prediction.py b/replicate/prediction.py
index 0e4d2349..a69217d8 100644
--- a/replicate/prediction.py
+++ b/replicate/prediction.py
@@ -21,7 +21,7 @@ class Prediction(BaseModel):
     created_at: Optional[str]
     completed_at: Optional[str]
 
-    def wait(self):
+    def wait(self) -> None:
         """Wait for prediction to finish."""
         while self.status not in ["succeeded", "failed", "canceled"]:
             time.sleep(self._client.poll_interval)
@@ -47,7 +47,7 @@ def output_iterator(self) -> Iterator[Any]:
         for output in new_output:
             yield output
 
-    def cancel(self):
+    def cancel(self) -> None:
         """Cancel a currently running prediction"""
         self._client._request("POST", f"/v1/predictions/{self.id}/cancel")
 
@@ -55,13 +55,30 @@ def cancel(self):
 class PredictionCollection(Collection):
     model = Prediction
 
-    def create(
+    def list(self) -> List[Prediction]:
+        resp = self._client._request("GET", "/v1/predictions")
+        # TODO: paginate
+        predictions = resp.json()["results"]
+        for prediction in predictions:
+            # HACK: resolve this? make it lazy somehow?
+            del prediction["version"]
+        return [self.prepare_model(obj) for obj in predictions]
+
+    def get(self, id: str) -> Prediction:
+        resp = self._client._request("GET", f"/v1/predictions/{id}")
+        obj = resp.json()
+        # HACK: resolve this? make it lazy somehow?
+        del obj["version"]
+        return self.prepare_model(obj)
+
+    def create(  # type: ignore
         self,
         version: Version,
         input: Dict[str, Any],
         webhook: Optional[str] = None,
         webhook_completed: Optional[str] = None,
         webhook_events_filter: Optional[List[str]] = None,
+        **kwargs,
     ) -> Prediction:
         input = encode_json(input, upload_file=upload_file)
         body = {
@@ -83,19 +100,3 @@ def create(
         obj = resp.json()
         obj["version"] = version
         return self.prepare_model(obj)
-
-    def get(self, id: str) -> Prediction:
-        resp = self._client._request("GET", f"/v1/predictions/{id}")
-        obj = resp.json()
-        # HACK: resolve this? make it lazy somehow?
-        del obj["version"]
-        return self.prepare_model(obj)
-
-    def list(self) -> List[Prediction]:
-        resp = self._client._request("GET", "/v1/predictions")
-        # TODO: paginate
-        predictions = resp.json()["results"]
-        for prediction in predictions:
-            # HACK: resolve this? make it lazy somehow?
-            del prediction["version"]
-        return [self.prepare_model(obj) for obj in predictions]
diff --git a/replicate/schema.py b/replicate/schema.py
index 34642cc3..a48d2351 100644
--- a/replicate/schema.py
+++ b/replicate/schema.py
@@ -3,12 +3,15 @@
 # TODO: this code is shared with replicate's backend. Maybe we should put it in the Cog Python package as the source of truth?
 
 
-def version_has_no_array_type(cog_version):
+def version_has_no_array_type(cog_version: str) -> bool:
     """Iterators have x-cog-array-type=iterator in the schema from 0.3.9 onward"""
     return version.parse(cog_version) < version.parse("0.3.9")
 
 
-def make_schema_backwards_compatible(schema, version):
+def make_schema_backwards_compatible(
+    schema: dict,
+    version: str,
+) -> dict:
     """A place to add backwards compatibility logic for our openapi schema"""
     # If the top-level output is an array, assume it is an iterator in old versions which didn't have an array type
     if version_has_no_array_type(version):
diff --git a/replicate/training.py b/replicate/training.py
index bf43a465..b60c9613 100644
--- a/replicate/training.py
+++ b/replicate/training.py
@@ -21,7 +21,7 @@ class Training(BaseModel):
     status: str
     version: str
 
-    def cancel(self):
+    def cancel(self) -> None:
         """Cancel a running training"""
         self._client._request("POST", f"/v1/trainings/{self.id}/cancel")
 
@@ -29,13 +29,25 @@ def cancel(self):
 class TrainingCollection(Collection):
     model = Training
 
-    def create(
+    def list(self) -> List[Training]:
+        raise NotImplementedError()
+
+    def get(self, id: str) -> Training:
+        resp = self._client._request(
+            "GET",
+            f"/v1/trainings/{id}",
+        )
+        obj = resp.json()
+        return self.prepare_model(obj)
+
+    def create(  # type: ignore
         self,
         version: str,
         input: Dict[str, Any],
         destination: str,
         webhook: Optional[str] = None,
         webhook_events_filter: Optional[List[str]] = None,
+        **kwargs,
     ) -> Training:
         input = encode_json(input, upload_file=upload_file)
         body = {
@@ -66,11 +78,3 @@ def create(
         )
         obj = resp.json()
         return self.prepare_model(obj)
-
-    def get(self, id: str) -> Training:
-        resp = self._client._request(
-            "GET",
-            f"/v1/trainings/{id}",
-        )
-        obj = resp.json()
-        return self.prepare_model(obj)
diff --git a/replicate/version.py b/replicate/version.py
index 02a5fa5d..d4ed9108 100644
--- a/replicate/version.py
+++ b/replicate/version.py
@@ -1,6 +1,11 @@
 import datetime
 import warnings
-from typing import Any, Iterator, List, Union
+from typing import TYPE_CHECKING, Any, Iterator, List, Union
+
+if TYPE_CHECKING:
+    from replicate.client import Client
+    from replicate.model import Model
+
 
 from replicate.base_model import BaseModel
 from replicate.collection import Collection
@@ -12,7 +17,7 @@ class Version(BaseModel):
     id: str
     created_at: datetime.datetime
     cog_version: str
-    openapi_schema: Any
+    openapi_schema: dict
 
     def predict(self, **kwargs) -> Union[Any, Iterator[Any]]:
         warnings.warn(
@@ -36,7 +41,7 @@ def predict(self, **kwargs) -> Union[Any, Iterator[Any]]:
             raise ModelError(prediction.error)
         return prediction.output
 
-    def get_transformed_schema(self):
+    def get_transformed_schema(self) -> dict:
         schema = self.openapi_schema
         schema = make_schema_backwards_compatible(schema, self.cog_version)
         return schema
@@ -45,7 +50,7 @@ def get_transformed_schema(self):
 class VersionCollection(Collection):
     model = Version
 
-    def __init__(self, client, model):
+    def __init__(self, client: "Client", model: "Model") -> None:
         super().__init__(client=client)
         self._model = model
 
@@ -59,6 +64,9 @@ def get(self, id: str) -> Version:
         )
         return self.prepare_model(resp.json())
 
+    def create(self, **kwargs) -> Version:
+        raise NotImplementedError()
+
     def list(self) -> List[Version]:
         """
         Return a list of all versions for a model.
diff --git a/requirements-dev.txt b/requirements-dev.txt
index c3865e8e..e23d31d9 100644
--- a/requirements-dev.txt
+++ b/requirements-dev.txt
@@ -2,7 +2,7 @@
 # This file is autogenerated by pip-compile with Python 3.11
 # by the following command:
 #
-#    pip-compile --extra=dev --output-file=requirements-dev.txt pyproject.toml
+#    pip-compile --extra=dev --output-file=requirements-dev.txt --resolver=backtracking pyproject.toml
 #
 attrs==22.2.0
     # via pytest
@@ -18,8 +18,12 @@ idna==3.4
     # via requests
 iniconfig==2.0.0
     # via pytest
+mypy==1.2.0
+    # via replicate (pyproject.toml)
 mypy-extensions==1.0.0
-    # via black
+    # via
+    #   black
+    #   mypy
 packaging==23.0
     # via
     #   black
@@ -48,7 +52,9 @@ ruff==0.0.261
 types-pyyaml==6.0.12.9
     # via responses
 typing-extensions==4.5.0
-    # via pydantic
+    # via
+    #   mypy
+    #   pydantic
 urllib3==1.26.15
     # via
     #   requests