This chapter provides a brief review of problems in contact dynamics between solids. Basic rheological models, the discrete elements method (DEM) as well as the problems of definition of the viscoelastic forces in cases of viscoelastic, elastic-plastic and high-elastic contacts are considered in this chapter. The simplified models of a viscoelastic sliding and rolling friction between surfaces of two solids are proposed. Boundary value problems and specifics of the initial and boundary conditions of loading and unloading of contacting surfaces are considered here as well.