we will discuss the possible closures of geodesic planes in a hyperbolic 3-manifold m. when m has finite volume shah and ratner (independently) showed that a strong rigidity phenomenon holds, and in particular such closures are always properly immersed submanifolds of m with finite area. we show that a similar rigidity phenomenon holds for a class of infinite volume manifolds. this is based on joint works with c. mcmullen and h. oh.