Chain of thought (CoT) fine-tuning aims to endow large language models (LLMs) with reasoning capabilities by training them on curated reasoning traces. It leverages both supervised and reinforced fine-tuning to cultivate human-like reasoning skills in LLMs, including detailed planning, divergent thinking, intuitive judgment, timely reflection, internal thinking, and fact perception, etc. As CoT fine-tuning has advanced, LLMs have demonstrated substantial improvements in tasks such as mathematical reasoning and code generation. However, existing surveys about CoT fine-tuning primarily focus on technical aspects and overlook a systematic analysis from the perspective of human reasoning mechanisms. Given that the ultimate goal of CoT fine-tuning is to enable LLMs to reason like humans, it is crucial to investigate this technique through the lens of human cognition. To fill this gap, we present the first comprehensive survey of CoT fine-tuning grounded in human reasoning theory. Specifically, inspired by the well-known Six Thinking Hats framework, which systematically characterizes common human thinking modes using six metaphorical hats, we classify and examine CoT fine-tuning methods through this lens. Furthermore, building upon this theory, we outline potential directions for future research in CoT fine-tuning. In addition, we compile a comprehensive overview of existing datasets and model performances, and a real-time GitHub repository \footnote{https://github.com/AI-Chen/Awesome-CoT-Finetuning} that continuously tracks recent advances in this area is maintained. We hope this survey will serve as a valuable resource to inspire innovation and foster progress in this rapidly evolving field.