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With the development of robotic, mobile manipulators are widely used in the fields of intelligent manufacturing, family service, agricultural picking, and epidemic protection and so on. The research on the motion planning method of mobile manipulator is conducive to the expansion of its application scene and the enhancement of its working ability, which has important academic research significance and social practical application value. Firstly, the relevant theories of mobile manipulators are introduced, and its kinematic modeling method is elaborated. On this basis, the research results of motion planning methods of mobile manipulators at the present stage are categorized and reviewed. According to the different underlying data structures and algorithmic ideas, it is classified into sampling-based, search-based, optimization-based, and learning-based planning methods for review; according to whether the overall planning is carried out or not, it is classified into decoupled planning and coordinated planning for review. Finally, the future development trend and research direction of mobile manipulator motion planning are discussed and outlooked.