I will describe an extension to the boundary of the cosphere bundle and geodesic flow of an asymptotically hyperbolic manifold. I will then discuss injectivity results for X-ray transforms on tensors and the boundary rigidity problem of determining an asymptotically hyperbolic metric from the renormalized lengths of geodesics joining boundary points. One part is work with Colin Guillarmou, Plamen Stefanov and Gunther Uhlmann and another part is work with Nikolas Eptaminitakis.