In recent years, the collaborative operation of multiple unmanned aerial vehicles (UAVs) has been an important advancement in drone technology. The research on multi-UAV collaborative flight path planning has garnered widespread attention in the drone field, demonstrating unique advantages in complex task execution, large-scale monitoring, and disaster response. As one of the core technologies of multi-UAV collaborative operations, the research and technological progress in trajectory planning algorithms directly impact the efficiency and safety of UAV collaborative operations. This paper first reviews the application and research progress of path-planning algorithms based on centralized and distributed control, as well as heuristic algorithms in multi-UAV collaborative trajectory planning. It then summarizes the main technical challenges in multi-UAV path planning and proposes countermeasures for multi-UAV collaborative planning in government, business, and academia. Finally, it looks to future research directions, providing ideas for subsequent studies in multi-UAV collaborative trajectory planning technology.