diff --git a/airflow/providers/amazon/aws/operators/glue.py b/airflow/providers/amazon/aws/operators/glue.py
index 053e530c72674..815dda8acd3e7 100644
--- a/airflow/providers/amazon/aws/operators/glue.py
+++ b/airflow/providers/amazon/aws/operators/glue.py
@@ -200,4 +200,4 @@ def execute(self, context: Context):
     def execute_complete(self, context, event=None):
         if event["status"] != "success":
             raise AirflowException(f"Error in glue job: {event}")
-        return
+        return event["value"]
diff --git a/airflow/providers/amazon/aws/operators/glue_crawler.py b/airflow/providers/amazon/aws/operators/glue_crawler.py
index c7ac25f1f2e30..5ba3dd0fcf4a9 100644
--- a/airflow/providers/amazon/aws/operators/glue_crawler.py
+++ b/airflow/providers/amazon/aws/operators/glue_crawler.py
@@ -107,4 +107,4 @@ def execute(self, context: Context):
     def execute_complete(self, context, event=None):
         if event["status"] != "success":
             raise AirflowException(f"Error in glue crawl: {event}")
-        return
+        return self.config["Name"]
diff --git a/airflow/providers/amazon/aws/triggers/glue.py b/airflow/providers/amazon/aws/triggers/glue.py
index 42219a993ad25..fbb4d83eb0c1f 100644
--- a/airflow/providers/amazon/aws/triggers/glue.py
+++ b/airflow/providers/amazon/aws/triggers/glue.py
@@ -60,4 +60,4 @@ def serialize(self) -> tuple[str, dict[str, Any]]:
     async def run(self) -> AsyncIterator[TriggerEvent]:
         hook = GlueJobHook(aws_conn_id=self.aws_conn_id)
         await hook.async_job_completion(self.job_name, self.run_id, self.verbose)
-        yield TriggerEvent({"status": "success", "message": "Job done"})
+        yield TriggerEvent({"status": "success", "message": "Job done", "value": self.run_id})
diff --git a/airflow/providers/amazon/aws/triggers/glue_crawler.py b/airflow/providers/amazon/aws/triggers/glue_crawler.py
index 10ab45dda73d3..3d058cf3f5b2f 100644
--- a/airflow/providers/amazon/aws/triggers/glue_crawler.py
+++ b/airflow/providers/amazon/aws/triggers/glue_crawler.py
@@ -68,10 +68,7 @@ async def run(self) -> AsyncIterator[TriggerEvent]:
                     break  # we reach this point only if the waiter met a success criteria
                 except WaiterError as error:
                     if "terminal failure" in str(error):
-                        yield TriggerEvent(
-                            {"status": "failure", "message": f"Glue Crawler creation Failed: {error}"}
-                        )
-                        break
+                        raise
                     self.log.info("Status of glue crawl is %s", error.last_response["Crawler"]["State"])
                     await asyncio.sleep(int(self.poll_interval))