Abstract: Both asteroid and comet exploration are important areas in the deep space exploration. The mass of an asteroid or a comet is not big enough, so its gravitational force is much smaller than the stress to satisfy the hydrostatic equilibrium, which makes the minor celestial body irregular-shaped. The research of dynamical behaviours and mechanisms in the gravitational field of irregular celestial body is the basis of minor celestial body exploration, including the catching of the explorer and the design of the orbit around the minor celestial body. This paper summarizes the research progress of the dynamics in the gravitational field of irregular celestial body through gravitational models and dynamical mechanisms. The research situation of gravitational models such as the Legendre polynomial model, the simple-shaped model and the polyhedron model are presented. In addition, the research situation of dynamical mechanisms such as the periodic orbits and quasi-periodic orbits, equilibrium points, manifolds, bifurcations and resonances, chaos, are also presented. Besides, we have analyzed key points and difficult points of these researches. Finally, the research trend of the dynamics in the gravitational field of irregular celestial body is discussed.