In applications to number theory, it is often desirable to find effective dynamical results. We want to provide effective information about averages of orbits of the horospherical subgroup acting on a hyperbolic manifold of infinite volume. We will start by presenting the setting and results for manifolds with finite volume. Then, we will discuss the difficulties that arise when studying the infinite volume setting, and the measures that play a crucial role in it. This is joint work with Jacqueline Warren.