diff --git a/swh/core/api/tests/test_rpc_client.py b/swh/core/api/tests/test_rpc_client.py
--- a/swh/core/api/tests/test_rpc_client.py
+++ b/swh/core/api/tests/test_rpc_client.py
@@ -6,12 +6,18 @@
 import re
 
 import pytest
+from requests.exceptions import ConnectionError
 
-from swh.core.api import RPCClient, remote_api_endpoint
+from swh.core.api import APIError, RemoteException, RPCClient, remote_api_endpoint
+from swh.core.api.serializers import exception_to_dict, msgpack_dumps
 
 from .test_serializers import ExtraType, extra_decoders, extra_encoders
 
 
+class ReraiseException(Exception):
+    pass
+
+
 @pytest.fixture
 def rpc_client(requests_mock):
     class TestStorage:
@@ -35,6 +41,7 @@
         backend_class = TestStorage
         extra_type_encoders = extra_encoders
         extra_type_decoders = extra_decoders
+        reraise_exceptions = [ReraiseException]
 
         def overridden_method(self, data):
             return "bar"
@@ -84,3 +91,64 @@
 def test_client_overridden_method(rpc_client):
     res = rpc_client.overridden_method("foo")
     assert res == "bar"
+
+
+def test_client_connexion_error(rpc_client, requests_mock):
+    error_message = "unreachable host"
+    requests_mock.post(
+        re.compile("mock://example.com/connection_error"),
+        exc=ConnectionError(error_message),
+    )
+
+    with pytest.raises(APIError) as exc_info:
+        rpc_client.post("connection_error", data={})
+
+    assert type(exc_info.value.args[0]) == ConnectionError
+    assert str(exc_info.value.args[0]) == error_message
+
+
+def _exception_response(exception, status_code):
+    def callback(request, context):
+        assert request.headers["Content-Type"] == "application/x-msgpack"
+        context.headers["Content-Type"] = "application/x-msgpack"
+        context.content = msgpack_dumps(exception_to_dict(exception))
+        context.status_code = status_code
+        return context.content
+
+    return callback
+
+
+def test_client_reraise_exception(rpc_client, requests_mock):
+    error_message = "something went wrong"
+    endpoint = "reraise_exception"
+
+    requests_mock.post(
+        re.compile(f"mock://example.com/{endpoint}"),
+        content=_exception_response(
+            exception=ReraiseException(error_message), status_code=400
+        ),
+    )
+
+    with pytest.raises(ReraiseException) as exc_info:
+        rpc_client.post(endpoint, data={})
+
+    assert str(exc_info.value) == error_message
+
+
+@pytest.mark.parametrize("status_code", [400, 500])
+def test_client_raise_remote_exception(rpc_client, requests_mock, status_code):
+    error_message = "something went wrong"
+    endpoint = "raise_remote_exception"
+
+    requests_mock.post(
+        re.compile(f"mock://example.com/{endpoint}"),
+        content=_exception_response(
+            exception=Exception(error_message), status_code=status_code
+        ),
+    )
+
+    with pytest.raises(RemoteException) as exc_info:
+        rpc_client.post(endpoint, data={})
+
+    assert str(exc_info.value.args[0]["type"]) == "Exception"
+    assert str(exc_info.value.args[0]["message"]) == error_message