(eng): This chapter reviews mathematical approaches to inelastic processes on the surfaces of elastic bodies. We mostly consider a quasistatic and rate-independent evolution at small strains. Various concepts of solutions are introduced and applied (including their comparison), e.g., to elastic-brittle delamination, cohesive contact problems, and to delamination in various fracture modes, or combined with friction. Besides the theoretical treatment, numerical experiments are also presented. Several implicit time discretization schemes are exploited. Finally, generalizations to dynamic and thermodynamic processes are outlined, together with an extension to the homogenization of composite materials with debonding phases.