  We give a criterion in terms of the boundary for the existence of a proper
cocompact action of a word-hyperbolic group on a CAT(0) cube complex. We
describe applications towards lattices and hyperbolic 3-manifold groups. In
particular, by combining the theory of special cube complexes, the surface
subgroup result of Kahn-Markovic, and Agol's criterion, we find that every
subgroup separable closed hyperbolic 3-manifold is virtually fibered.
