With the continuous development of UAV technology and swarm intelligence technology, the UAV formation cooperative mission has attracted wide attention because of its remarkable function and flexibility to complete complex and changeable tasks, such as search and rescue, resource exploration, reconnaissance and surveillance. The collaborative trajectory planning of UAV formation is a key part of the task execution. This paper attempts to provide a comprehensive review of UAV formation trajectory planning algorithms. Firstly, from the perspective of global planning and local planning, a simple framework of the UAV formation trajectory planning algorithm is proposed, which is the basis of comprehensive classification of different types of algorithms. According to the proposed framework, a classification method of existing UAV formation trajectory planning algorithms is proposed, and then, different types of algorithms are described and analyzed statistically. Finally, the challenges and future research directions of the UAV formation trajectory planning algorithm are summarized and prospected according to the actual requirements. It provides reference information for researchers and workers engaged in the formation flight of UAVs.