The space deployable mechanism is widely used to develop and support the flexible solar array and payloads including parabolic antenna, plane phased array radar, and synthetic aperture radar in the aerospace engineering field. Non-smooth characteristics and the corresponding dynamic phenomena play a very important role in the design of space deployable mechanism. This paper reviews the state-of-art of non-smooth mechanical modeling and nonlinear dynamics for the space deployable mechanisms. First of all, the non-smooth properties such as the contact impact forces and friction models are elaborated for hinges with clearances. Then, the dynamical modeling methods, analytical approach, and parametric design are systematically presented for the mechanisms with clearances. Moreover, the nonlinear dynamic phenomena such as harmonic resonance, existence and stability of periodic motions, and various kinds of bifurcations are presented for the space deployable mechanisms whose joints are with clearances. Finally, directions for further works on the dynamics, stability and control for the non-smooth dynamical system of space deployable mechanisms are proposed.