We discuss some recent techniques for establishing the uniqueness of equilibrium states for certain classes of dynamical systems (developed in joint work with Climenhaga). The technique is based on studying on-uniform versions of certain properties from hyperbolic dynamics. These techniques are rather robust, and can be applied in settings of geometric interest, including geodesic flow on rank one manifolds (in joint work with Burns, Climenhaga, Fisher), and geodesic flow on CAT(-1) spaces (in joint work with Constantine and Lafont). I'll introduce some of the main ideas, and give an idea of how they can be applied. Speaker(s): Daniel Thompson (Ohio State University)