Due to decades of unremitting efforts, China's aviation and space technology has gradually become advanced in the world. However, the complex and changeable space environment and the inherent physical properties of the flexible arm itself often cause a series of problems to the end-effector, like vibrating or failing to follow the prescribed path. Based on a brief description of the development status quo of space flexible robotic arm technology at home and abroad, the research status of space flexible robotic arm were analyzed in three aspects: modeling, control methods and trajectory planning, and the design methods applicable to relevant contents under different working conditions, their advantages and disadvantages were investigated in detail, as well as the specific application of this method by some experts and scholars. Finally, according the above analysis, the development trend and prospect of flexible space manipulator were proposed.