2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/64034We mostly survey results concerning the $L^2$ boundedness of oscillatory and Fourier integral operators. This article does not intend to give a broad overview; it mainly focusses on a few topics directly related to the work of the authors.37 pages, to appear in Publicacions Mathematiques (special issue, Proceedings of the 2000 El Escorial Conference in Harmonic Analysis and Partial Differential Equations)Classical Analysis and ODEstext