Quantum spin Hall systems and topological insulators

Topological insulators (quantum spin Hall systems) are insulating in the bulk but have gapless edge/surface states, which remain gapless even when nonmagnetic disorder or interaction is present. This robustness stems from the topological nature characterized by the Z(2) topological number, and this offers us various kinds of new novel properties. We review prominent advances in theories and in experiments on topological insulators since their theoretical proposal in 2005.