The crew schedule is a crucial component of urban rail transit operation plannings, and its optimization methods have become a hot research topic in the field of transportation. To promote the research progress in crew planning optimization for urban rail transit, reviewing relevant literatures from both domestic and international sources. Regarding mathematical models, systematically summarizing two typical modeling approaches which are respectively based on "set relations" and "network graph construction"; Concerning solution algorithms, provideing detailed assessments of traditional integer programming algorithm, mathematical programming method based on column generation, graph and network-related algorithm, and intelligent heuristic algorithm. Finally, addressing current research deficiencies and challenges to propose future research directions.