  The class of topological insulator materials is one of the frontier topics of
condensed matter physics. The great success of this field is due to the
conceptual breakthroughs in theories for topological electronic states and is
strongly motivated by the rich variety of material realizations, thus making
the theories testable, the experiments operable, and the applications possible.
First-principles calculations have demonstrated unprecedented predictive power
for material selection and design. In this article, we review recent progress
in this field with a focus on the role of first-principles calculations. In
particular, we introduce the Wilson loop method for the determination of
topological invariants and discuss the band inversion mechanism for the
selection of topological materials. Recent progress in quantum anomalous Hall
insulators, large-gap quantum spin Hall insulators, and correlated topological
insulators are also covered.

Mesoscale and Nanoscale Physics