Underwater video compression is one of the key technologies for transmitting massive amount of real-time video data via underwater acoustic channels with limited bandwidth. The authors first describe the major problems involved in the development of underwater robots and underwater video compression, then comprehensively analyze the characteristics of several efficient video-coding methods, and finally discuss the future research directions. According to the characteristics of underwater imaging, they propose a potential hybrid global-local motion compensation scheme and a wavelet transform based a preprocessing method. Preparatory experimental results show that the proposed preprocessing method could effectively remove the visual and spatial redundancy of underwater images and the proposed hybrid compensation scheme could achieve a very high compression ratio. Further investigation is necessary for a fast and robust computing method of global motion.