As the core equipment for deep-sea aquaculture, the hydrodynamic research on ship-shaped aquaculture cages is crucial for ensuring their structural safety and farming reliability under extreme sea conditions. This paper systematically integrates the framework of "theoretical research-numerical simulation-model validation" used in the hydrodynamic study of ship-shaped aquaculture cages and reviews the relevant hydrodynamic analysis theories. The research status is reviewed from three aspects: hydrodynamic responses of the hull and mooring system, hull structural strength, and fluid-structure interaction effects of the netting. Furthermore, the key challenges in the hydrodynamic analysis of ship-shaped cages are analyzed: the complexity of multi-physics strong-coupling modeling, the accuracy-efficiency trade-offs in netting simulation, the bottlenecks in predicting nonlinear responses under extreme environments, and the lack of full-scale validation data. Finally, four future research directions are proposed: developing a multi-field wave-structure-mooring-netting interaction model, advancing the refined modeling technology for complex marine environments such as typhoons and internal waves, introducing intelligent algorithms to optimize the dynamic response of mooring systems, and developing hydrodynamic optimization and control technologies for intelligent submersible systems. This review provides theoretical support for the hydrodynamic mechanism research and engineering safety application of ship-shaped aquaculture cages.