  We prove two results relating 3-manifold groups to fundamental groups
occurring in complex geometry. Let N be a compact, connected, orientable
3-manifold. If N has non-empty, toroidal boundary, and \pi_1(N) is a Kaehler
group, then N is the product of a torus with an interval. On the other hand, if
N has either empty or toroidal boundary, and \pi_1(N) is a quasi-projective
group, then all the prime components of N are graph manifolds.
