This article explores the abilities of large language models (LLMs) in identifying and correcting their reasoning mistakes, particularly in Chain-of-Thought (CoT) reasoning. It introduces the BIG-Bench Mistake dataset for evaluating LLMs' error detection and examines their performance in four key areas: detecting logical mistakes in CoT reasoning, using error detection as a correctness measure, correcting known errors, and generalizing mistake identification to new tasks. The findings highlight the current limitations of LLMs in mistake detection but suggest promise in backtracking methods for corrections and the potential of specialized models for improved error identification across different tasks.