  This 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.
