Large Language Models (LLMs) have demonstrated remarkable abilities to solve problems requiring multiple reasoning steps, yet the internal mechanisms enabling such capabilities remain elusive. Unlike existing surveys that primarily focus on engineering methods to enhance performance, this survey provides a comprehensive overview of the mechanisms underlying LLM multi-step reasoning. We organize the survey around a conceptual framework comprising seven interconnected research questions, from how LLMs execute implicit multi-hop reasoning within hidden activations to how verbalized explicit reasoning remodels the internal computation. Finally, we highlight five research directions for future mechanistic studies.