A group G is called coherent if every finitely generated subgroup of G is finitely presented.  This is a property enjoyed by the fundamental groups of 3-manifolds, and it is deeply related to the geometry of the group. We show that free-by-free groups satisfying a particular homological criterion are incoherent. This class is large in nature, including many examples of hyperbolic and non-hyperbolic free-by-free groups. We apply this criterion to finite index subgroups of $F_2\rtimes F_n$ to show incoherence of all such groups, and to other similar classes of groups.   This is joint work with Rob Kropholler.