Abstract: Given a finitely generated, non-elementary discrete subgroup G < Isom(H^n), the orbit points grow exponentially with respect to the hyperbolic distance, and the critical exponent of G is defined to be the exponential growth rate. In this talk, I will present recent joint work with Beibei Liu. We show that if the critical exponent is small enough, then G is convex-cocompact, that is, the orbit map is a quasi-isometric embedding. Along the way, I'll also explain how a small critical exponent affects the geometry and topology of the quotient space.