  In this paper, we establish a number of results about the topology of the
leaves of a closed singular Riemannian foliation $(M,\fol)$. If $M$ is simply
connected, we prove that the leaves are finitely covered by nilpotent spaces,
and characterize the fundamental group of the generic leaves. If $M$ has
virtually nilpotent fundamental group, we prove that the leaves have virtually
nilpotent fundamental group as well.
