Geodesics in hyperbolic space, or more generally in an asymptotically hyperbolic manifold, have infinite length as they approach the boundary at infinity.  Nonetheless, it is possible to associate a finite renormalized length to such a geodesic.  This talk will describe how one can recover the infinite order boundary jet of an asymptotically hyperbolic metric up to isometry if one knows the renormalized lengths of geodesics connecting nearby boundary points. Analytically, the problem reduces to recovering information from divergent integrals constructed from solutions of the ordinary differential equations determining the geodesics.  This is joint work with Plamen Stefanov and Gunther Uhlmann.