The thesis is mainly focused on three topics: modeling of contact problems, \(h\)- and \(hp\)-finite element discretisation and a posteriori error control for contact problems and adaptivity. The author considers some model problems of Signorini type, idealized friction problems, and – as a problem of production engineering – contact problems for an industrial robot supported belt grinding. Furthermore, applications to other modeling problems are discussed. An important aspect, which has to be investigated, is the verification of the obtained results by numerical experiments.