The industrialization, high-density, and greener aquaculture requires a more precise and intelligent aquaculture management. Phenotypic and behavioral information of fish, which can reflect fish growth and welfare status, play a crucial role in aquaculture management. Stereo vision technology, which simulates parallax perception of the human eye, can obtain the three-dimensional phenotypic characteristics and movement trajectories of fish through different types of sensors. It can overcome the limitations in dealing with fish deformation, frequent occlusions and understanding three-dimension scenes compared to the traditional two-dimensional computer vision techniques. With the deep learning development and application in aquaculture, stereo vision has become a super computer vision technology that can provide more precise and interpretable information for intelligent aquaculture management, such as size estimation, counting and behavioral analysis of fish. Hence, it is very beneficial for researchers, managers, and entrepreneurs to possess a thorough comprehension about the fast-developing stereo vision technology for modern aquaculture. This study provides a critical review of relevant topics, including the four-layer application structure of stereo vision technology in aquaculture, various deep learning-based technologies used, and specific application scenarios. The review contributes to research development by identifying the current challenges and provide valuable suggestions for future research directions. This review can serve as a useful resource for developing future studies and applications of stereo vision technology in smart aquaculture, focusing on phenotype feature extraction and behavioral analysis of fish. full text