The principle of holography provides us with well defined models of quantum gravity within string theory. These models of gravity contain black holes, but we do not yet have a complete holographic description of the interior of these black holes. I will describe this problem, and its relation to questions in statistical mechanics and quantum information theory. I will also describe how this problem provides us with some hints of surprising new physical effects.
Most of this talk will be at an elementary level, and designed to introduce students to this field of research.