As a new type of carrier, the unmanned aerial underwater vehicle (UAUV) has the ability to fly in the air, navigate underwater, and actively enter and exit the water multiple times. It can play a unique role in military and civilian fields such as submarine warfare, communication relay, and ocean remote sensing. In recent years, it has received widespread attention from researchers in various fields. This paper summarizes the types of prototypes and technical routes, and believes that the current research focus of UAUVs should be on folding-wing and hybrid UAUVs. The key issues should be in the process of water entry and exit and underwater navigation. This paper proposes targeted solutions for the research on the stability near sea surface, trajectories and loads during fast water entry and exit, and underwater navigation mechanics, and provides guidance for future development and practical applications.