As marine resources continue to be exploited, the remarkable locomotion and coordination of fish provide an excellent source of inspiration for scientists and engineers to design and control the next -generation autonomous underwater vehicles within a bionic framework. Underwater biomimetic robots combine bionics and robot technology, and their biological characteristics offer a lot of convenience for the robot so that it can obtain better performance in adaptability and robustness. Recently, with the combination of bionics, mechanics, electronics, materials science, and automation, there has been great progress in developing underwater bionic robots with different structure types and energy supply modes. This paper summarizes the research status of underwater robots, focuses on the research status of underwater bionic robots with different materials, types and motion modes, and introduces the propulsion mechanism of underwater robots with different structures and the control methods adopted in the propulsion process. Finally, the broad application prospect and market potential of underwater biomimetic robot are introduced.