Self-correction is an approach to improving responses from large language models (LLMs)  by refining the responses using LLMs during inference. Prior work has proposed various self-correction frameworks using different sources of feedback, including self-evaluation and external feedback. However, there is still no consensus on the question ofwhen LLMs can correct their own mistakes, as recent studies also report negative results. In this work, we critically survey broad papers and discuss the conditions required for successful self-correction. We first find that prior studies often do not define their research questions in detail and involve impractical frameworks or unfair evaluations that over-evaluate self-correction. To tackle these issues, we categorize research questions in self-correction research and provide a checklist for designing appropriate experiments. Our critical survey based on the newly categorized research questions shows that (1)  no prior work demonstrates successful self-correction with feedback from prompted LLMs in general tasks, (2)  self-correction works well in tasks that can use reliable external feedback, and (3)  large-scale fine-tuning enables self-correction.