The underwater hexapod robot has redundant limbs, and can walk in various gaits. It has a broad application prospect for its discrete supporting way and excellent adaptability to the complex and special terrains(underwater obstacles, reefs, etc). The development status of underwater hexapod robot platform is summarized in this paper, based on sufficient literature research and summary. Aiming at the crawling ability of underwater hexapod robot, three key technologies are analyzed and summarized respectively, including stability criteria, path planning, and adaptive walking method. For stability criteria, the static and dynamic stability criteria of underwater hexapod robot are described respectively. Based on the current typical path planning methods of land hexapod robot, the path planning of underwater hexapod robot is described according to its unique motion characteristics. For the adaptive walking of underwater hexapod robot, the traditional adaptive adjustment methods and the current methods based on deep reinforcement learning are introduced respectively. Finally, the future development trends of these key technologies are prospected.