Abstract Real-time obstacle avoidance is the basis to ensure the safe operation of the autonomous underwater vehicle (AUV), and it also represents the intelligent level of AUV. The main factors that affect AUV obstacle avoidance are environment perception ability, obstacle avoidance decision-making ability, and trajectory tracking control ability. This paper starts from the perspective of obstacle avoidance decision-making ability, that is, obstacle avoidance algorithm. Firstly, we summarized the structure and influencing factors of AUV real-time obstacle avoidance. Then, we introduced in detail the research progress of AUV intelligent obstacle avoidance algorithms, including fuzzy logic algorithms, neural network algorithms, and reinforcement learning algorithms. And we analysed the improvement methods of each algorithm from three-dimensional underwater environment, ocean current, AUV motion characteristics, and dynamic obstacles. Finally, we prospected the development of the AUV intelligent obstacle avoidance algorithm.