In this review, the development of techniques for determining the plasticity of materials by the indentation is considered. The development of methods for determining the plasticity of materials by the indentation is based on the use of fundamental ideas of the physics of strength and plasticity. Significant development of these methods became possible after the introduction of a new plasticity characteristic $\delta^{*} = \epsilon_{р}/\epsilon_{t}$, where $\epsilon_{р}$ is the plastic deformation, and $\epsilon_{t}$ is the total deformation. This plasticity characteristic corresponds to the modern physical definitions of plasticity, in contrast to the widely used elongation to failure $\delta$. The new plasticity characteristic is easily determined by standard determination of hardness by the diamond pyramidal indenters at constant load $P$ (designated as $\delta_{Н}$) and by instrumental nanoindentation (designated as $\delta_{А}$, and $\delta_{Н} \approx \delta_{А}$). A significant advantage of the new plasticity characteristic is the ability to determine it not only for metals, but for materials, which are brittle at the standard mechanical tests (ceramics, thin layers, coatings, etc.), as well. In the development of ideas about theoretical strength, concepts of theoretical plasticity under the dislocation-free and dislocation deformation mechanisms are introduced. A number of studies have established a correlation of $\delta_{Н}$ with the electronic structure of the material and its physical properties. As shown, the Tabor parameter $С$ ($C = HM/\sigma_{S}$, where $HM$ is the Meyer hardness, and $\sigma_{S}$ is the yield stress) is easily calculated by the $\delta_{Н}$ value. Therefore, indentation allows currently determining simply not only the hardness, but also the plasticity and yielding stress of materials. Thus, indentation became a simple method for determination of the complex of mechanical properties of materials in a wide temperature range using a sample in the form of a metallographic specimen.