In this talk I will focus on the class of surface bundles over a surface. Such groups are a natural extension of fibered 3-manifolds. We are Zusammenfassung: interested in what properties surface-by-surface groups have in common with fibered 3-manifold groups. Of particular interest is the question of fibering and incoherence. I will discuss the relations between these properties and use this to show that a such a bundle has coherent fundamental group if and only if the base is a torus. I will also discuss obstructions to such bundles' algebraic fibering. This is joint work with Stefano Vidussi and Genevieve Walsh.