The swarm operation of unmanned marine vehicle (UMV) has been developed and evolved from concept to practical application. In view of the mission requirements of UMV swarms, this paper summarizes the development of the UMV swarm concepts of unmanned aerial vehicle (UAV), unmanned surface vehicle (USV) and unmanned underwater vehicle (UUV), and cross-domain swarm operations of UMV in naval warfare. It then analyzes the key technologies of UMV swarm cooperative engagement, including self-organizing communication, collaborative situational awareness, tasking, path planning, formation control and virtual testing. Finally, the main research ideas, representative algorithms and development trends of the related algorithms are summarized systematically. This study can provide valuable references for research on UMV swarm operation technology.