The paper gives a review of publications on models of hysteresis in problems of mechanics and technical physics. The main known approaches are listed and described briefly indicating their applications. Describing the hysteresis, the authors suggest the mathematical models based on a concrete understanding of a physical phenomenon. It is noted that despite the specificity of the models, a number of them can be used to describe other processes different by their nature. The classical models for problems of structural dynamics, elastic-plastic deformation, rheological fluids behavior are considered. The static friction models are summarized. There are marked peculiarities of the dynamic friction models, which take into account the Stribeck effect, hysteresis of surface microplastic deformations, irregular sliding, etc. The phenomenological models under consideration are used to describe a variety of hysteresis effects in nature. In this case, the system is considered as a “black box” with experimental values of input and output parameters known. Correlations between them are established on the basis of mathematical functions, whose parameters are identified using experimental data. The models are often based on spectral resolution by the relay nonlinearities. It is the Bouc-Wen model to be marked among the phenomenological ones, which is typically used in the frames of the “black box”. Currently, this model and its analogues are successfully used in various scientific and technical fields due to their possibility of the analytical description of various shapes of hysteresis loops. There are formulated in literature the conditions which must be satisfied while applying the Bouc-Wen model. The main ones are the mathematical model adequacy to the physical process under consideration and stability. The article also pointed out a number of original hysteresis models, whose possibilities go beyond the specialized application. The article also points out a number of original hysteresis models, whose possibilities go beyond the frames of their specialized application.