While large language models (LLMs) have shown remarkable effectiveness in various NLP tasks, they are still prone to issues such as hallucination, unfaithful reasoning, and toxicity. A promising approach to rectify these flaws is correcting LLMs with feedback , where the LLM itself is prompted or guided with feedback to fix problems in its own output. Techniques leveraging automated feedback —either produced by the LLM itself (self-correction) or some external system—are of particular interest as they make LLM-based solutions more practical and deployable with minimal human intervention. This paper provides an exhaustive review of the recent advances in correcting LLMs with automated feedback, categorizing them into training-time, generation-time, and post-hoc approaches. We also identify potential challenges and future directions in this emerging field.