Abstract: This paper aims to review systematically the theory and numerical methods for dynamic contact problems over the recent twenty years. The dynamic contact problem is a new subject in the contact mechanics. Many numerical methods have been developed up to now, such as (1) the Lagrange multiplier method the penalty method the perturbed Lagrange method, theaugmented Lagrange method; (2) the linear complementary method; (3) the joint element method,(4) the dynamic contact force method;(5) the impulse model, the dynamic contact model, the initialdisplacement model, ect. The foundamental control equations and the dynamic contact conditionsneeded in the dynamic contact analysis are summarized in the paper. Principles of the methods areaddressed and the numerical results based on these methods are presented and evaluated. Finally,some research directions and potential engineering applications are suggested.