Cross-media vehicles have become a research hotspot in the field of aerospace-ship interaction because of their high concealment, strong maneuverability and fast penetration by switching between water and air working modes. Sea-air medium crossing involves multiphase flow mixing, unsteady evolution of cavitation and harsh load environment, which threaten the motion stability, water attitude and structural strength of vehicles. Aiming at problems of evolution characteristics of the shoulder/exhaust cavity flow and the tail cavity, and the collapse and load characteristics of the cross water-air medium during the cross-medium water exit process of the vehicle, this paper expounds the research status of the mechanism of the shoulder/tail cavity flow during the underwater navigation and water exit process of the cross-medium vehicle in the aerospace-ship crossover field in recent years. The research on the collapse and load characteristics of the cross sea-air medium process is summarized, and the cross domain water exit problems involving different launch environments are listed. Finally, the problems to be solved and the future development trend in the field of aerospace-ship crossover are summarized and discussed.