Description The most studied are three-webs and their special classes and characteristics. The three-web formed by foliations of condimension p, q, r on a manifold of dimension P Q is denoted by W (p, q, r). In case p= q= r, the closure of sufficiently small configurations of a certain type on the web W (r, r, r) corresponds to some identity in the coordinate quasigroup f. It was W. Blaschke and his colleagues K. Reidemeister, G. Thomsen, G. Bol, and others, who began the study of the differential-topological theory of webs in 1920s-1930s. The study of multidimensional three-webs continued with the work of G. Bol (1935-1936), S.S. Chern (1936), M. Akivis (since 1969), V. V. Goldberg (since 1973) and others. In this review the author also describes the configurations that arise at the boundary of a curved three-web and fractal structures that naturally arise on a curvilinear three-web