2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/209569This paper is a survey on the {\em Zimmer program}. In it's broadest form, this program seeks an understanding of actions of large groups on compact manifolds. The goals of this survey are $(1)$ to put in context the original questions and conjectures of Zimmer and Gromov that motivated the program, $(2)$ to indicate the current state of the art on as many of these conjectures and questions as possible and $(3)$ to indicate a wide variety of open problems and directions of research.Survey article, 84 pages, almost final version, comments welcome but only if made quicklyDynamical SystemsDifferential GeometryGroup Theory37C85; 53C24text