Multi-agent path finding (MAPF) aims to plan conflict-free paths for multiple agents to optimize collaborative task performance. This study reviews the current state of MAPF research, including algorithm classification, application scenarios, and future trends, while discussing the challenges in large-scale dynamic environments. First, the study provides a detailed introduction to the definition of MAPF. Then, it categorizes and summarizes path planning algorithms based on search, bio-inspired methods, sampling, and reinforcement learning. Finally, the study analyzes the advantages and disadvantages of each algorithm and their applicable scenarios. This review aims to help researchers understand the current developments and future directions of MAPF technology, and to promote further progress in this field.