2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/122696This is an expositiry article on collapsing theory in Riemannian geometry written for the Modern Encyclopedia of Mathematical Physics (MEMPhys). We focus on describing the geometric and topological structure of collapsed/non-collapsed regions in Riemannian manifold under various curvature assumptions. Numerous applications of collapsing theory to Riemannian geometry are NOT discussed in this survey.references added, 11 pagesDifferential Geometry53C20text