Satellite communication has the characteristics of wide coverage and large communication capacity, and is not easily affected by land disasters. It is quite suitable as a supplement to terrestrial communication networks and has been widely used in education, navigation, emergency relief, military, etc. However, due to the openness of the channel of satellite communication systems, satellite communication signals are easily eavesdropped on by eavesdroppers. This greatly threatens the privacy and security of countries and individuals. Covert satellite communication can effectively improve the covertness of satellite communication systems and greatly reduce the probability of detection by eavesdroppers. So, it has attracted more and more attention. In addition, with the development of artificial intelligence (AI), AI has been applied in many technics of covert satellite communication, which has achieved higher reliability and stronger concealment in covert satellite communication systems. The research status of key technics in covert satellite communication is discussed in this study, and the applications of AI in covert satellite communication are shown. Finally, future research directions of covert satellite communication are looked forward to. In the future, covert satellite communication technology will be an indispensable part of satellite communication systems.