We study the geodesic flow on the unit tangent bundle of a rank one manifold and we give conditions under which all classical definitions of pressure of a Hoelder continuous potential coincide. We provide a large deviation statement, which allows to neglect (periodic) orbits that lack sufficient hyperbolic behaviour. Our results involve conditions on the potential, which take into consideration its properties in the non-hyperbolic part of the manifold. We draw some conclusions for the construction of equilibrium states. This is joint work with Barbara Schapira.