Satellite clusters, as a distributed collaborative spacecraft system, possess significant application value in areas such as Earth observation, on-orbit assembly, and deep space exploration. Given the constraints of the dynamic space environment and limited on-orbit computing resources, the primary challenge is to devise an effective technique for cluster trajectory planning to ensure the successful execution of cluster tasks. Based on typical satellite cluster systems both domestically and internationally, related application scenarios and developmental tendencies were summarized. The development status of satellite cluster trajectory planning methods was comprehensively elaborated. From the perspectives of Euclidean space and manifold space, the advantages and disadvantages of existing methods were discussed. Starting from recent popular machine learning techniques, the development status of satellite cluster trajectory planning methods that combine deep learning and reinforcement learning with traditional approaches was introduced. Finally, the challenges were encapsulated, and future research avenues were anticipated.