Nowadays energy storage systems (ESS) are becoming an integral part of modern power systems (PES) and are used to solve a wide range of tasks. However, as the penetration level and power of ESS grows, their impact on the processes and operation modes of EPS is also increasing. Therefore, there is a need for using mathematical models of ESS, taking into account the specifics, various distinctive properties of each type and class of EPS, as part of the models of large-scale EPS. However, in foreign and national literature there are no review papers about detailed mathematical models of commonly use types and classes of SNE and simplifications used for them, which can be used to adequately simulate the large-scale EPS depending on the research tasks. Therefore, the first part of this paper considers the most promising types and classes of SNE used in the EPS, as well as the a-reas and tasks of their use. The principles of implementation of detailed mathematical models and structures of automatic control systems are described for the considered types and classes of SNE. In the second part of the paper the modern approaches of simplification of mathematical models of SNE, and analysis of consequences of such simplifications and areas of their application are given. Thus, the review paper consists of two parts and can help in choosing a mathematical model of the SNE for solving specific research tasks of analysis of their operation as a part of real EPS.