Abstract: The binary asteroid systems, consisting of two asteroids orbiting each other through the mutual gravitation, are of great significance for studying the origin of our solar system and the evolution of planetary systems, as well as for the planetary defense. Therefore, binary asteroid systems have become a hot research topic of the planetary science and astrodynamics, and several in situ exploration missions will be launched in the near future. The unique configurations and complex dynamical environments of binary asteroid systems have brought about new challenges for orbital dynamics and the mission design. The studies devoted to the new challenges have greatly promoted the development of basic theories of orbital mechanics. In this paper, we review and summarize the research progress on orbital dynamics about the binary asteroid system exploration. We first introduce the background and significance of the binary asteroid system exploration, and briefly review the formation theory and the research status of orbital dynamics about binary asteroid systems. Secondly, the modeling methods for the irregular gravity field and the mutual gravitational potential of binary asteroid systems are introduced. The coupled orbit-attitude motion of two members of the binary system, i.e., the full two-body problem, including the equilibrium configurations and their stability, is also discussed. Thirdly, the concept and applications of the restricted full three-body problem about binary asteroid systems are introduced, including the libration points and associated periodic orbits, general periodic orbits, transfer orbits, and station-keeping strategies. In the fourth part, the secular orbital evolution around one member of a binary asteroid system is focused from viewpoint of the perturbed two-body problem. The perturbation theory and applications in planetary systems are illustrated first, and then some recent research on the semi-analytical orbital model and stability analysis around the primary of a binary asteroid system is presented. Fifthly, the orbital dynamics analyses and the mission design for near future exploration missions, considering mission objectives and practical constraints, are summarized. Finally, based on the current research progress, challenges and prospects of orbital dynamics and related technologies about the binary asteroid system exploration are discussed.