abstract: A Kaehler-Weyl manifold is a complex manifold that satisfies a weakened version of the Kaehler condition arising in conformal geometry. We will discuss generalizations of various results about the existence of holomorphic fibrations from compact Kaehler manifolds to Kaehler-Weyl manifolds. As an application we obtain constraints on the fundamental groups of such manifolds. (Joint work with G. Kokarev.)