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Current sheets (CSs) are the important objects in space plasma separating the regions with different magnetic characteristics. They can accumulate magnetic energy and release it via magnetic reconnection. Numerous observations of the CSs in the Earth's magnetotail provide much information on their spatial structure and evolution. Multipoint spacecraft observations demonstrated that the CSs often exhibit complicated multiscale structure in which a thin and intense current layer is embedded in a thicker layer(s) having a smaller current density. To describe these features the quasi-adiabatic approach is more effective than the classical MHD approximation. Thin current sheet features, such as embedding, asymmetry of the current density spatial profiles, metastability, has been predicted by the kinetic approach and subsequently confirmed "in situ" observations. The role of individual particle populations in the formation of the CS fine structure has also been investigated. CSs are observed in different objects of space plasma, e.g. in the terrestrial and Martian magnetospheres, in the solar wind and exhibit very similar characteristic features in their spatial structures, despite the drastic difference in the formation mechanisms and local plasma characteristics. This phenomenon can be explained by the universal mechanism of their formation in different natural conditions. Once CS has been formed, then it should be self-consistently supported by the internal coupling of the total current carried by particles in the CS and its magnetic configuration, and as soon as the system achieved the quasi-equilibrium state, it "forgets" the mechanisms of its initial formation, and its emerging structures controlled only by the general principles of plasma kinetics described by Vlasov- Maxwell equations.