diff --git a/CHANGELOG.md b/CHANGELOG.md
index cc67a31b..fbb08d4b 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -10,12 +10,14 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 ### Changed
 
 - BREAKING: Renamed `function` field of the Function pydantic model to `archive`([#393](https://github.com/Substra/substra/pull/393))
-- BREAKING: Renamed ComputeTask status ([#397](https://github.com/Substra/substra/pull/397))
+- BREAKING: Renamed ComputeTask status values ([#397](https://github.com/Substra/substra/pull/397))
 - `download_logs` uses the new endpoint ([#398](https://github.com/Substra/substra/pull/398))
+- BREAKING: Renamed Status to ComputeTaskStatus ([#399](https://github.com/Substra/substra/pull/399))
 
 ### Added
 
 - Paths are now resolved on DatasampleSpec objects. Which means that users can pass relative paths ([#392](https://github.com/Substra/substra/pull/392))
+- Added FunctionStatus ([#399](https://github.com/Substra/substra/pull/399))
 
 ## [0.49.0](https://github.com/Substra/substra/releases/tag/0.49.0) - 2023-10-18
 
diff --git a/references/sdk.md b/references/sdk.md
index 7cc92c7f..6814d2c6 100644
--- a/references/sdk.md
+++ b/references/sdk.md
@@ -546,7 +546,7 @@ The ``filters`` argument is a dictionary, with those possible keys:
     rank (List[int]): list tasks which are at given ranks.
 
     status (List[str]): list tasks with given status.
-        The possible values are the values of `substra.models.Status`
+        The possible values are the values of `substra.models.ComputeTaskStatus`
     metadata (dict)
         {
             "key": str # the key of the metadata to filter on
diff --git a/references/sdk_models.md b/references/sdk_models.md
index 8d6b757b..40fecad7 100644
--- a/references/sdk_models.md
+++ b/references/sdk_models.md
@@ -48,7 +48,7 @@ Asset creation specification base class.
 - owner: <class 'str'>
 - compute_plan_key: <class 'str'>
 - metadata: typing.Dict[str, str]
-- status: <enum 'Status'>
+- status: <enum 'ComputeTaskStatus'>
 - worker: <class 'str'>
 - rank: typing.Optional[int]
 - tag: <class 'str'>
diff --git a/substra/sdk/backends/local/backend.py b/substra/sdk/backends/local/backend.py
index 0ae914d5..4ccd2225 100644
--- a/substra/sdk/backends/local/backend.py
+++ b/substra/sdk/backends/local/backend.py
@@ -301,6 +301,7 @@ def _add_function(self, key, spec, spec_options=None):
             metadata=spec.metadata if spec.metadata else dict(),
             inputs=_schemas_list_to_models_list(spec.inputs, models.FunctionInput),
             outputs=_schemas_list_to_models_list(spec.outputs, models.FunctionOutput),
+            status=models.FunctionStatus.ready,
         )
         return self._db.add(function)
 
@@ -429,7 +430,7 @@ def _add_task(self, key, spec, spec_options=None):
             outputs=_output_from_spec(spec.outputs),
             tag=spec.tag or "",
             # TODO: the waiting status should be more granular now
-            status=models.Status.waiting_for_executor_slot,
+            status=models.ComputeTaskStatus.waiting_for_executor_slot,
             metadata=spec.metadata if spec.metadata else dict(),
         )
 
diff --git a/substra/sdk/backends/local/compute/worker.py b/substra/sdk/backends/local/compute/worker.py
index 7933ed65..33ff40eb 100644
--- a/substra/sdk/backends/local/compute/worker.py
+++ b/substra/sdk/backends/local/compute/worker.py
@@ -255,7 +255,7 @@ def schedule_task(self, task: models.Task):
             task: Task to execute
         """
         with self._context(task.key) as task_dir:
-            task.status = models.Status.doing
+            task.status = models.ComputeTaskStatus.doing
             task.start_date = datetime.datetime.now()
             function = self._db.get_with_files(schemas.Type.Function, task.function.key)
             input_multiplicity = {i.identifier: i.multiple for i in function.inputs}
@@ -377,7 +377,7 @@ def schedule_task(self, task: models.Task):
                 )
 
             # Set status
-            task.status = models.Status.done
+            task.status = models.ComputeTaskStatus.done
             task.end_date = datetime.datetime.now()
 
             self._update_cp(compute_plan=compute_plan, update_live_performances=update_live_performances)
diff --git a/substra/sdk/backends/local/dal.py b/substra/sdk/backends/local/dal.py
index e422d10f..af34161e 100644
--- a/substra/sdk/backends/local/dal.py
+++ b/substra/sdk/backends/local/dal.py
@@ -123,7 +123,7 @@ def get_performances(self, key: str) -> models.Performances:
         performances = models.Performances()
 
         for task in list_tasks:
-            if task.status == models.Status.done:
+            if task.status == models.ComputeTaskStatus.done:
                 function = self.get(schemas.Type.Function, task.function.key)
                 perf_identifiers = [
                     output.identifier for output in function.outputs if output.kind == schemas.AssetKind.performance
diff --git a/substra/sdk/client.py b/substra/sdk/client.py
index b0ea924c..82bc273b 100644
--- a/substra/sdk/client.py
+++ b/substra/sdk/client.py
@@ -763,7 +763,7 @@ def list_task(
             worker (List[str]): list tasks which ran on listed workers. Remote mode only.\n
             rank (List[int]): list tasks which are at given ranks.\n
             status (List[str]): list tasks with given status.
-                The possible values are the values of `substra.models.Status`
+                The possible values are the values of `substra.models.ComputeTaskStatus`
             metadata (dict)
                 {
                     "key": str # the key of the metadata to filter on
@@ -1062,9 +1062,46 @@ def wait_task(
                 Not raised when `timeout == None`
         """
         asset_getter = self.get_task
-        status_canceled = models.Status.canceled.value
-        status_failed = models.Status.failed.value
-        statuses_stopped = (models.Status.done.value, models.Status.canceled.value)
+        status_canceled = models.ComputeTaskStatus.canceled.value
+        status_failed = models.ComputeTaskStatus.failed.value
+        statuses_stopped = (models.ComputeTaskStatus.done.value, models.ComputeTaskStatus.canceled.value)
+        return self._wait(
+            key=key,
+            asset_getter=asset_getter,
+            polling_period=polling_period,
+            raise_on_failure=raise_on_failure,
+            status_canceled=status_canceled,
+            status_failed=status_failed,
+            statuses_stopped=statuses_stopped,
+            timeout=timeout,
+        )
+
+    @logit
+    def wait_function(
+        self, key: str, *, timeout: Optional[float] = None, polling_period: float = 1.0, raise_on_failure: bool = True
+    ) -> models.Task:
+        """Wait for the build of the given function to finish.
+
+        It is considered finished when the status is ready, failed or cancelled.
+
+        Args:
+            key (str): the key of the task to wait for.
+            timeout (float, optional): maximum time to wait, in seconds. If set to None, will hang until completion.
+            polling_period (float): time to wait between two checks, in seconds. Defaults to 2.0.
+            raise_on_failure (bool): whether to raise an exception if the execution fails. Defaults to True.
+
+        Returns:
+            models.Task: the task after completion
+
+         Raises:
+            exceptions.FutureFailureError: The task failed or have been cancelled.
+            exceptions.FutureTimeoutError: The task took more than the duration set in the timeout to complete.
+                Not raised when `timeout == None`
+        """
+        asset_getter = self.get_function
+        status_canceled = models.FunctionStatus.canceled.value
+        status_failed = models.FunctionStatus.failed.value
+        statuses_stopped = (models.FunctionStatus.ready.value, models.FunctionStatus.canceled.value)
         return self._wait(
             key=key,
             asset_getter=asset_getter,
@@ -1095,7 +1132,7 @@ def _wait(
             if asset.status in statuses_stopped:
                 break
 
-            if asset.status == models.Status.failed.value and asset.error_type is not None:
+            if asset.status == models.ComputeTaskStatus.failed.value and asset.error_type is not None:
                 # when dealing with a failed task, wait for the error_type field of the task to be set
                 # i.e. wait for the registration of the failure report
                 break
diff --git a/substra/sdk/models.py b/substra/sdk/models.py
index e82d780a..8b9c00e7 100644
--- a/substra/sdk/models.py
+++ b/substra/sdk/models.py
@@ -30,7 +30,7 @@ class MetadataFilterType(str, enum.Enum):
     exists = "exists"
 
 
-class Status(str, enum.Enum):
+class ComputeTaskStatus(str, enum.Enum):
     """Status of the task"""
 
     unknown = "STATUS_UNKNOWN"
@@ -57,6 +57,17 @@ class ComputePlanStatus(str, enum.Enum):
     empty = "PLAN_STATUS_EMPTY"
 
 
+class FunctionStatus(str, enum.Enum):
+    """Status of the function"""
+
+    unknown = "FUNCTION_STATUS_UNKNOWN"
+    waiting = "FUNCTION_STATUS_WAITING"
+    building = "FUNCTION_STATUS_BUILDING"
+    ready = "FUNCTION_STATUS_READY"
+    failed = "FUNCTION_STATUS_FAILED"
+    canceled = "FUNCTION_STATUS_CANCELED"
+
+
 class TaskErrorType(str, enum.Enum):
     """Types of errors that can occur in a task"""
 
@@ -178,6 +189,7 @@ class Function(_Model):
     creation_date: datetime
     inputs: List[FunctionInput]
     outputs: List[FunctionOutput]
+    status: FunctionStatus
 
     description: _File
     archive: _File
@@ -268,7 +280,7 @@ class Task(_Model):
     owner: str
     compute_plan_key: str
     metadata: Dict[str, str]
-    status: Status
+    status: ComputeTaskStatus
     worker: str
     rank: Optional[int] = None
     tag: str
diff --git a/tests/datastore.py b/tests/datastore.py
index 2b5a230f..9847d77e 100644
--- a/tests/datastore.py
+++ b/tests/datastore.py
@@ -78,6 +78,7 @@
         "opener": {"kind": "ASSET_DATA_MANAGER", "optional": False, "multiple": False},
     },
     "outputs": {"model": {"kind": "ASSET_MODEL", "multiple": False}},
+    "status": "FUNCTION_STATUS_READY",
 }
 
 
@@ -106,6 +107,7 @@
         "shared": {"kind": "ASSET_MODEL", "optional": True, "multiple": False},
     },
     "outputs": {"predictions": {"kind": "ASSET_MODEL", "multiple": False}},
+    "status": "FUNCTION_STATUS_READY",
 }
 
 
@@ -133,6 +135,7 @@
         "predictions": {"kind": "ASSET_MODEL", "optional": False, "multiple": False},
     },
     "outputs": {"performance": {"kind": "ASSET_PERFORMANCE", "multiple": False}},
+    "status": "FUNCTION_STATUS_READY",
 }
 
 
@@ -162,6 +165,7 @@
             "opener": {"kind": "ASSET_DATA_MANAGER", "optional": False, "multiple": False},
         },
         "outputs": {"model": {"kind": "ASSET_MODEL", "multiple": False}},
+        "status": "FUNCTION_STATUS_READY",
     },
     "owner": "MyOrg1MSP",
     "creation_date": "2021-08-24T13:36:07.393646367Z",
@@ -234,6 +238,7 @@
         "metadata": {"foo": "bar"},
         "inputs": {"model": {"kind": "ASSET_MODEL", "optional": False, "multiple": True}},
         "outputs": {"model": {"kind": "ASSET_MODEL", "multiple": False}},
+        "status": "FUNCTION_STATUS_READY",
     },
     "owner": "MyOrg1MSP",
     "creation_date": "2021-08-24T13:36:07.393646367Z",
@@ -308,6 +313,7 @@
             "local": {"kind": "ASSET_MODEL", "multiple": False},
             "shared": {"kind": "ASSET_MODEL", "multiple": False},
         },
+        "status": "FUNCTION_STATUS_READY",
     },
     "owner": "MyOrg1MSP",
     "creation_date": "2021-08-24T13:36:07.393646367Z",
@@ -420,6 +426,7 @@
             "local": {"kind": "ASSET_MODEL", "multiple": False},
             "shared": {"kind": "ASSET_MODEL", "multiple": False},
         },
+        "status": "FUNCTION_STATUS_READY",
     },
     "owner": "MyOrg1MSP",
     "creation_date": "2021-08-24T13:36:07.393646367Z",
@@ -478,6 +485,7 @@
             "shared": {"kind": "ASSET_MODEL", "optional": True, "multiple": False},
         },
         "outputs": {"predictions": {"kind": "ASSET_MODEL", "multiple": False}},
+        "status": "FUNCTION_STATUS_READY",
     },
     "owner": "MyOrg1MSP",
     "creation_date": "2021-08-24T13:36:07.393646367Z",
@@ -536,6 +544,7 @@
             "predictions": {"kind": "ASSET_MODEL", "optional": False, "multiple": False},
         },
         "outputs": {"performance": {"kind": "ASSET_PERFORMANCE", "multiple": False}},
+        "status": "FUNCTION_STATUS_READY",
     },
     "owner": "MyOrg1MSP",
     "creation_date": "2021-08-24T13:36:07.393646367Z",
diff --git a/tests/sdk/test_wait.py b/tests/sdk/test_wait.py
index 58c14ecf..9e7204b7 100644
--- a/tests/sdk/test_wait.py
+++ b/tests/sdk/test_wait.py
@@ -4,7 +4,7 @@
 
 from substra.sdk import exceptions
 from substra.sdk.models import ComputePlanStatus
-from substra.sdk.models import Status
+from substra.sdk.models import ComputeTaskStatus
 from substra.sdk.models import TaskErrorType
 
 from .. import datastore
@@ -21,8 +21,8 @@ def _param_name_maker(arg):
 @pytest.mark.parametrize(
     ("asset_dict", "function_name", "status", "expectation"),
     [
-        (datastore.TRAINTASK, "wait_task", Status.done, does_not_raise()),
-        (datastore.TRAINTASK, "wait_task", Status.canceled, pytest.raises(exceptions.FutureFailureError)),
+        (datastore.TRAINTASK, "wait_task", ComputeTaskStatus.done, does_not_raise()),
+        (datastore.TRAINTASK, "wait_task", ComputeTaskStatus.canceled, pytest.raises(exceptions.FutureFailureError)),
         (datastore.COMPUTE_PLAN, "wait_compute_plan", ComputePlanStatus.done, does_not_raise()),
         (
             datastore.COMPUTE_PLAN,
@@ -49,7 +49,7 @@ def test_wait(client, mocker, asset_dict, function_name, status, expectation):
 
 def test_wait_task_failed(client, mocker):
     # We need an error type to stop the iteration
-    item = {**datastore.TRAINTASK, "status": Status.failed, "error_type": TaskErrorType.internal}
+    item = {**datastore.TRAINTASK, "status": ComputeTaskStatus.failed, "error_type": TaskErrorType.internal}
     mock_requests(mocker, "get", item)
     with pytest.raises(exceptions.FutureFailureError):
         client.wait_task(key=item["key"])
@@ -58,9 +58,9 @@ def test_wait_task_failed(client, mocker):
 @pytest.mark.parametrize(
     ("asset_dict", "function_name", "status"),
     [
-        (datastore.TRAINTASK, "wait_task", Status.waiting_for_parent_tasks),
-        (datastore.TRAINTASK, "wait_task", Status.waiting_for_builder_slot),
-        (datastore.TRAINTASK, "wait_task", Status.waiting_for_executor_slot),
+        (datastore.TRAINTASK, "wait_task", ComputeTaskStatus.waiting_for_parent_tasks),
+        (datastore.TRAINTASK, "wait_task", ComputeTaskStatus.waiting_for_builder_slot),
+        (datastore.TRAINTASK, "wait_task", ComputeTaskStatus.waiting_for_executor_slot),
         (datastore.COMPUTE_PLAN, "wait_compute_plan", ComputePlanStatus.todo),
     ],
     ids=_param_name_maker,
diff --git a/tests/test_utils.py b/tests/test_utils.py
index 46019b4f..29f302e9 100644
--- a/tests/test_utils.py
+++ b/tests/test_utils.py
@@ -81,8 +81,8 @@ def test_check_metadata_search_filter(filters, expected, exception):
         ),
         (
             schemas.Type.Task,
-            {"status": [substra.models.Status.done.value]},
-            {"status": [substra.models.Status.done.value]},
+            {"status": [substra.models.ComputeTaskStatus.done.value]},
+            {"status": [substra.models.ComputeTaskStatus.done.value]},
             None,
         ),
         (schemas.Type.Task, {"rank": [1]}, {"rank": ["1"]}, None),