Advanced composite structures have been widely applied in aircraft. Compared with traditional metallic materials, their application not only enables the lightweight aircraft design but also enhances damage tolerance. The harsh service environment and complex load conditions pose severe challenges to the aerospace composite structures. Therefore, health monitoring of composite structures has become an inevitable way to ensure the in-service safety of aircraft. This paper analyzes the damage mechanism and typical damage modes of composite structures, and introduces the health monitoring requirements of aerospace composite structures. Regarding the monitoring of macroscopic and microscopic damage, health status, and lifespan of aircraft composite structures, the application status of traditional monitoring methods is summarized. Research progress of advanced structural health monitoring (SHM) technologies, such as flexible electronic skins and selfpowered sensors, is introduced. Innovative application of intelligence technologies such as multi-sensor data fusion technology, digital twin and machine learning in the SHM system of aerospace composite structures is also discussed. A brief overview of the practical engineering applications of SHM technology in aerospace sector, both domestically and internationally, is presented, and the future research priorities for its future development directions and intelligence are discussed, which offers reference for the research on the health monitoring of aerospace composite structures.