  Topological insulators represent a new quantum state of matter which is
characterized by peculiar edge or surface states that show up due to a
topological character of the bulk wave functions. This review presents a
pedagogical account on topological insulator materials with an emphasis on
basic theory and materials properties. After presenting a historical
perspective and basic theories of topological insulators, it discusses all the
topological insulator materials discovered as of May 2013, with some
illustrative descriptions of the developments in materials discoveries in which
the author was involved. A summary is given for possible ways to confirm the
topological nature in a candidate material. Various synthesis techniques as
well as the defect chemistry that are important for realizing bulk-insulating
samples are discussed. Characteristic properties of topological insulators are
discussed with an emphasis on transport properties. In particular, the Dirac
fermion physics and the resulting peculiar quantum oscillation patterns are
discussed in detail. It is emphasized that proper analyses of quantum
oscillations make it possible to unambiguously identify surface Dirac fermions
through transport measurements. The prospects of topological insulator
materials for elucidating novel quantum phenomena that await discovery conclude
the review.
