Appears in collection : Riemannian Geometry Past, Present and Future: an homage to Marcel Berger

We show that the boundary distance function determine a simply connected surface with no conjugate points and that the lens data determine a non-trapping surface with no conjugate points. The novelty is that the manifold is not assumed to be « simple », i.e the boundary is not assumed convex. We also show new result on the geodesic ray transform when there is trapped set. This is joint work with Mazzucchelli and Tzou.