This paper discusses some of the main developments in our understanding of indentation hardness during the last 20 years and indicates the limitations of several current models. In particular, it deals critically with the expanding spherical cavity as applied to elastic-plastic solids and to solids with marked creep. It also discusses the problem of load application, the indentation behavior of single crystals, the hardness of semiconductors, and recent developments in crack formation by indentations in plastic-brittle solids. Finally, it deals with the more specific problem of hardness at extremely small loads and the practical as well as theoretical difficulties involved in characterizing microhardness in terms of depth of penetration.