Path planning is a key technology for autonomous underwater vehicle (AUV) navigation. With the emphasis and research on AUV, AUV path planning technology is continuously developing. Path planning techniques generally include environment modelling methods and path planning algorithms. Based on a brief description of the environment modelling methods, this paper focuses on the path planning algorithms commonly used by AUV. According to the basic principles of the algorithm, the AUV path planning algorithms are divided into four categories: artificial potential field methods, geometric model search methods, random sampling methods, and intelligent bionic methods. In this review, we summarize in detail the development and application of various path planning algorithms in recent years. Meanwhile, we analyse the advantages and disadvantages of various algorithms and their improvement methods. Obstacles, ocean currents, and undersea terrain have an impact on AUV path planning. Therefore, how to deal with the complex underwater environment adds some limits to AUV path planning algorithms. In addition to the external environment, path planning algorithms also need to consider AUV’s physical constraints, such as energy constraints and motion constraints. Then, we analyse the motion constraints in AUV path planning. Finally, we discuss the development direction of AUV path planning algorithm. Time-varying ocean currents, special obstacles, multiobjective constraints, and practicability will be the problems that AUV path planning algorithms need to solve.