Four years ago, the Nobel Prize in physics was awarded for "for theoretical discoveries of topological phase transitions and topological phases of matter." In line with this, I heard of topological insulators, a new material with the strange property of having an insulating bulk with a conductor surface, having a great interest because they could be useful for many future applications in electronics and quantum computation.
I would like to know what is a topological insulator from a theoretical point of view, i.e., how to recognize one from its band structure and how is the property of bulk-insulator/surface-conductor explained from first principles (at least conceptually).