2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/68894We give a brief survey of the concept of birational rigidity, from its origins in the two-dimensional birational geometry, to its current state. The main ingredients of the method of maximal singularities are discussed. The principal results of the theory of birational rigidity of higher-dimensional Fano varieties and fibrations are given and certain natural conjectures are formulated.24 pages, to appear in the Proceedings of Fano conferenceAlgebraic Geometry14E05; 14E07; 14E08text