Abstract: Asteroid exploration has become an important part of interplanetary missions because of its important scientific significances and engineering values. However, difficulties such as irregular gravity, unknown physical parameters and low escape velocity of asteroids make guidance and control in the vicinity of asteroids very challenging. In this paper, the history, current status and significances of asteroid missions are introduced. Then,the dynamics in the vicinity of asteroids, which are the foundation for studying the guidance and control in the vicinity of asteroids,are introduced. Thereafter,the hot issues and research status of methods of guidance and control for different missions which include hovering, parking orbits, orbit transfer, and landing are discussed in detail. In the conclusion,some relevant directions and problems for future researches are listed based on the research status.