in this talk we 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 very strong rigidity phenomenon holds, and in particular such closures are always properly immersed submanifolds of m with finite area. manifolds with infinite volume, however, are far less understood and are the main subject of this talk. this is based on a joint ongoing work with c. mcmullen and h. oh.