The marked length spectrum of a closed Riemannian manifold of negative curvature records the lengths of closed geodesics, and conjecturally determines the metric up to isometry. For constant curvature metrics on a genus g surface, 6g-5 geodesics are enough to fully recover the marked length spectrum. In the general case, Karen Butt recently showed that the marked length spectrum is almost determined by its restriction to a sufficiently large finite set of closed geodesics. I will talk about a joint work with Stephen Cantrell in which we extend Butt's work to the setting of marked length spectra of isometric actions of hyperbolic groups on Gromov hyperbolic spaces.