Let M be a manifold that admits a nontrivial cover diffeomorphic to itself. What can we then say about M? Examples are provided by tori, in which case the covering is a linear endomorphism. Under the assumption that all iterates of the covering of M are regular, we show that any self-cover is induced by a linear endomorphism of a torus on a quotient of the fundamental group. Under further hypotheses we show that M admits the structure of a principal torus bundle. We use this to give an application to holomorphic self-covers of Kaehler manifolds. Speaker(s): Wouter Van Limbeek (University of Michigan)