Autonomous vehicles hold the potential to significantly improve traffic efficiency and advance the development of intelligent transportation systems. With the progression of autonomous driving technology, collaborative planning among multiple vehicles in autonomous driving scenarios has emerged as a pivotal challenge in realizing intelligent transportation systems. Serving as the cornerstone of unmanned mission decision-making, collaborative motion planning algorithms have garnered increasing attention in both theoretical exploration and practical application. These methods often follow a similar paradigm: the system initially discerns the driving intentions of each vehicle, subsequently assesses the surrounding environment, engages in path-planning, and formulates specific behavioral decisions. The paper discusses trajectory prediction, game theory, following behavior, and lane merging issues within the paradigm mentioned above. After briefly introducing the background of multi-vehicle autonomous driving, it provides a detailed description of the technological prerequisites for implementing these techniques. It reviews the main algorithms in motion planning, their functionalities, and applications in road environments, as well as current and future challenges and unresolved issues.