We define a notion of hyperplane at infinity for a hyperbolic group G and study G-invariant Radon measures on the space of hyperplanes at infinity, which we call ``co-geodesic currents´´. Co-geodesic currents are induced by many classical objects such as geodesic currents for surface groups, certain cocompact actions of hyperbolic groups on CAT(0) cube complexes, some actions of hyperbolic groups on real trees, etc. Moreover, there is a natural intersection pairing between co-geodesic currents and geodesic currents, generalizing Bonahon's intersection number when G is a surface group. Furthermore, every co-geodesic current \mu induces natural dual pseudo-metric space with a measured wall structure, in the sense that the intersection of \mu with the current determined by the conjugacy class of an element g in G recovers the stable length of g in the pseudo-metric space. This is joint work in progress with Eduardo Reyes.