Google Cloud Functions handle retrying on failure through two methods: automatic and manual. Automatic retries occur when a function execution fails due to unhandled exceptions or timeouts, with the system automatically attempting to re-execute the function. Manual retries are initiated by the developer using the “retry” option in the Google Cloud Console, gcloud command-line tool, or Cloud Functions API. The number of retries is not limited but exponential backoff between attempts is applied to prevent overloading.