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 of when 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, except for studies in tasks that are exceptionally suited for self-correction, (2) self-correction works well in tasks that can use reliable external feedback, and (3) large-scale fine-tuning enables self-correction.