The work of Farb−Mosher and Hamenstädt provides a necessary and sufficient condition for the fundamental group of a closed surface bundle over any compact space to be word-hyperbolic. The condition is geometric in nature, involving the monodromy homomorphism and the action on Teichmuller space. Gromov's hyperbolization question, in the special case of surface bundles, asks whether the condition on the action can be relaxed to a topological one. In this talk I will discuss this problem, and some joint work with Bestvina, Bromberg, and Kent providing results in this direction.