Abstract: The algorithm studied for multi-agent path finding (MAPF) problem has wide applications in the fields of outdoor hazardous areas, intelligent warehousing system, and urban road networks. According to different solving approaches, the algorithms designed for MAPF problems can be mainly divided into two categories: traditional search-based algorithms and intelligent learning-based algorithms. In traditional search-based algorithm research, it can be divided into optimal MAPF algorithm and suboptimal MAPF algorithm according to different path planning effects. The optimal MAPF algorithm is mainly divided into three types: A^*-based search, increasing cost tree search (ICTS), and conflict-based search (CBS). The suboptimal MAPF algorithm is mainly divided into two categories: unbounded suboptimal algorithms and bounded suboptimal algorithms. Learning-based intelligent MAPF algorithms can be roughly divided into two categories: algorithms that combine expert experience and algorithms based on graph neural networks (GNN). Based on the above classification, the representative research results in recent years have been introduced. The characteristics of various algorithms are analyzed, and the future research directions of the MAPF problem are prospected.