  Singular fibrations generalize achiral Lefschetz fibrations of 4-manifolds
over surfaces while sharing some of their properties. For instance, relatively
minimal singular fibrations are determined by their monodromy. We explain how
to construct examples of singular fibrations with a single singularity and
Matsumoto's construction of singular fibrations of the sphere $S^4$. Previous
results of Hirzebruch and Hopf on 2-plane fields with finitely many
singularities are outlined in connection with the work of Neumann and Rudolph
on the Hopf invariant. Eventually, we prove that closed orientable 4-manifolds
with large first Betti number and vanishing second Betti number do not admit
singular fibrations.
