Abstract: For certain classes of insulating materials, it is possible to derive a very precise connection between properties of the bulk and properties of the surface. A connection of this kind is known as a bulk-boundary correspondence. While such correspondences can be very useful, unfortunately the only cases where they are understood in generality involve either non-interacting or low dimensional systems. In this talk, I will discuss progress on the bulk-boundary correspondence for a large class of three dimensional, interacting systems. Specifically, the systems I will discuss are known as symmetry-protected topological phases and can be thought of as generalizations of topological insulators and superconductors.