  In this paper we investigate what kind of manifolds arise as the total spaces
of iterated $S^1$-bundles. A real Bott tower studied in \cite{CMO}, \cite{KM}
and \cite{KN} is an example of an iterated $S^1$-bundle. We show that the total
space of an iterated $S^1$-bundle is homeomorphic to an infra-nilmanifold. A
real Bott manifold, which is the total space of a real Bott tower, provides an
example of a closed flat Riemannian manifold. We also show that real Bott
manifolds are the only closed flat Riemannian manifolds obtained from iterated
$\bbr{P}^1$-bundles. Finally we classify the homeomorphism types of the total
spaces of iterated $S^1$-bundles in dimension 3.
