Redundant　space　manipulators　(RSM)　exhibit　high　flexibility　and　can　assist　astronauts　in　completing　various　on-orbit　service　(OOS)　tasks,　which　have　been　applied　to　the　International　Space　Station　(ISS)　and　China　Space　Station　(CSS).　Motion　planning　stands　as　a　fundamental　technology　within　RSM,　guiding　the　manipulator　to　reach　designated　positions　smoothly　and　execute　operational　tasks　with　optimal　performance.　Nevertheless,　the　intricate　nature　of　the　space　environment　presents　challenges　to　the　motion　planning　of　RSM.　In　this　paper,　in　response　to　issues　such　as　maintenance　difficulties　after　RSM　failures,　base　floating　caused　by　weightlessness,　flexible　deformation　of　structures　due　to　large-scale　operations,　and　multiple　obstacles　with　uncertainty,　fault-tolerant　motion　planning,　motion　planning　considering　base　floating,　motion　planning　under　structural　flexibility　deformation,　and　obstacle　avoidance　motion　planning　are　examined.　At　present,　the　increasingly　complex　OOS　tasks　have　brought　new　challenges　to　the　motion　planning　of　RSM.　These　challenges　encompass　motion　planning　for　new　mechanism　configurations,　dynamic　motion　planning,　multi-RSM　and　multi-task　planning,　the　improvement　of　motion　planning　efficiency,　and　the　efficient　implementation　and　precise　process　monitoring　of　motion.　With　the　advancement　of　motion　planning　technology,　RSM　is　poised　to　play　an　increasingly　significant　role　in　ISS　and　CSS.