Contact-impact problems are of great interest in many engineering fields, eg automotive industry, aircraft industry, nuclear industry, defence industry, and ocean engineering etc. Much research work, both theoretical and experimental, has been carried out on the problem. The fast development of computational mechanics and computing techniques has made it possible to attack extremely complicated contact-impact problems with great success. It is the purpose of this paper to review the contact-impact problems and some recent developments in numerical studies on the problem. General descriptions and variational formulation of the problem are first given. Then, general finite element procedures and various techniques to solve the problem are discussed. Special attention is paid to the treatment of contact-impact interfaces. Finally, a bibliography on the contact-impact problem is presented, listing about five hundred reports, papers and books which have been published retrospectively from 1980.