Bionic robots possess inherent advantages for underwater operations, and research on motion control and intelligent decision making has expanded their application scope. In recent years, the application of reinforcement learning algorithms in the field of bionic underwater robots has gained considerable attention, and continues to grow. In this paper, we present a comprehensive survey of the accomplishments of reinforcement learning algorithms in the field of bionic underwater robots. Firstly, we classify existing reinforcement learning methods and introduce control tasks and decision making tasks based on the composition of bionic underwater robots. We further discuss the advantages and challenges of reinforcement learning for bionic robots in underwater environments. Secondly, we review the establishment of existing reinforcement learning algorithms for bionic underwater robots from different task perspectives. Thirdly, we explore the existing training and deployment solutions of reinforcement learning algorithms for bionic underwater robots, focusing on the challenges posed by complex underwater environments and underactuated bionic robots. Finally, the limitations and future development directions of reinforcement learning in the field of bionic underwater robots are discussed. This survey provides a foundation for exploring reinforcement learning control and decision making methods for bionic underwater robots, and provides insights for future research.