Topological insulators are a recently discovered quantum electronic phase of matter. This talk will give a brief overview of the known electronic phases of matter, focusing on the unique properties of topological insulators and their discovery from a careful consideration of the low energy electronic physics of single-layer graphene. Closely related topological ideas are then used to analyze the mysterious electronic behavior of a family of multilayer graphenes known as “twisted” graphenes in which a rotation of neighboring layers leads to unexpectedly rich low energy physics.