Geodesic planes in hyperbolic 3-manifolds

Let M be a hyperbolic 3-manifold, a geodesic plane in M is a totally geodesic immersion of 
the hyperbolic plane into M. In this talk we will give an overview of results which highlight how 
geometric, topological, and arithmetic properties of M are related to behavior of geodesic planes in M.
This talk is based on joint projects with McMullen and Oh, and in another direction with Margulis.