An overview of development of indentation techniques and connections between contact mechanics and methods of extracting mechanical characteristics from indentation data is given. Observed disagreements between the experimental observations and the models of indentation are discussed. It is shown that this disagreement is often caused by violation of hypotheses that are used in the formulation of the appropriate boundary-value contact problems and strictly speaking one cannot apply directly the solutions of Hertz type contact problems to indentation tests employing the sharp indenters. It is shown that commonly used experimental test involving sharp pyramidal and conical indenters may be applied to study plastic properties of materials while this approach is not very accurate for estimations of elastic modulus of the test solid. The recently proposed by Borodich and Galanov non-direct method that employs data of elastically loading of a spherical indenter is described. It is argued that the non-direct method can be used for determination of both the work of adhesion and elastic modulus of the tested material.