Underwater video images, as the primary carriers of underwater information, play a vital role in human exploration and development of the ocean. Due to the optical characteristics of water bodies, underwater video images generally have problems such as color bias and unclear image quality, and image quality degradation is severe. Degenerated images have adverse effects on the visual tasks of underwater vehicles, such as recognition and detection. Therefore, it is vital to obtain high-quality underwater video images. Firstly, this paper analyzes the imaging principle of underwater images and the reasons for their decline in quality and briefly classifies various existing methods. Secondly, it focuses on the current popular deep learning technology in underwater image enhancement, and the underwater video enhancement technologies are also mentioned. It also introduces some standard underwater data sets, common video image evaluation indexes and underwater image specific indexes. Finally, this paper discusses possible future developments in this area.