Abstract: The exploration of the moon and deep space objects or environment is an important field of human space activities. The exploration of the moon and deep space is conducive to the study of the origin, evolution and current situation of the solar system, the origin and evolution of life and other major scientific issues, and to the birth of basic and forward-looking disciplines and technologies. Compared with other detection methods such as optics, radar has the advantages of strong penetration, polarization and is not limited by light. It is one of the effective means to detect the characteristics of the moon and deep space objects and plays an important role in the exploration process. Electromagnetic wave can penetrate several meters to several thousand meters of subsurface, which can be used to detect the surface dielectric constant, subsurface structure, ionosphere and water ice of the moon and deep space targets. According to different detection methods, surface penetrating radar detection mainly includes ground-based radar, space-borne radar and rover radar. For different scientific objectives, different detection methods have their own advantages and disadvantages. Our review covers the retrospect of the scientific application of surface penetrating radar in the exploration of moon, Mars and asteroids, summarizes the exploration tasks, parameter design, working principle and results of various radar on-board different exploration missions, both planed ones and those in service, and looks forward to the development trend of lunar and deep space exploration using surface penetrating radar in the future.