A relevant interpretation of sharp indentation experiments requires a fundamental understanding of the mechanics involved in the process. Such understanding can only be achieved if an appropriate mechanical model is used in order to describe the problem. These models can in rare cases be purely analytical but nowadays numerical modeling is also a vital part of a mechanical approach. Furthermore, with the development of new materials and also nanoindentation devices, material (constitutive) modeling becomes very important. The aim of the present paper is first of all to present an overview of the state of the art of modeling of sharp indentation experiments. In particular indentation of classical Mises elastoplastic behaviour but also modeling of indentation of other types of materials will be touched upon. In addition, some fundamental issues of substantial importance at indentation modeling will be discussed. These issues include 1) the influence from large deformations, 2) differences and similarities between cone and pyramid indentation results, 3) the influence from residual stresses, 4) the effective elastic modulus at indentation and 5) differences and similarities between indentation and scratch results. Most of the results presented in these discussions have been published previously in international journals but the implications of these results have, in the authors opinion, not been fully appreciated by the indentation community, or at least not sufficiently discussed.