A group G is said to commensurate a subgroup H if [H: H\cap H^g] is finite for all g. Commensurated subgroups generalize normal subgroups. Let H be a non-elementary hyperbolic commensurated subgroup of infinite index in a hyperbolic group G. We show that H is virtually a free product of hyperbolic surface groups and free groups. This generalizes a theorem that goes back to work of Bestvina, Paulin, Rips, Sela when H is genuinely normal in G, using actions of H on R-trees. But when H is only commensurated, we need new techniques as such actions are unavailable. We also describe restrictions on the electrified graph obtained by electrifying cosets of H. This is joint work with Nir Lazarovich and Alex Margolis.