Recent developments in modeling of clearance joints and dynamics of mechanical systems with clearances are reviewed. Different modeling approaches for clearance joints are summarized firstly, which comprise the massless link approach, the non-smooth dynamics approach, the contact force approach and the 3D revolute joint approach. Then, applications of these approaches in the study of the nonlinear dynamics, and performance and reliability evaluation of the mechanical systems with clearances are systematically reviewed. Finally, the key problems and priorities which need to be further studied are proposed, including the modeling of clearace joints considering stick-slip phenomenon, contact surface profile and conformal contact condition, the dynamic analysis and kinematic accuracy evaluation of mechanical systems with both clearances and uncertainties, and the design for clearance joints.