  Topological phases with insulating bulk and gapless surface or edge modes
have attracted much attention because of their fundamental physics implications
and potential applications in dissipationless electronics and spintronics. In
this review, we mainly focus on the recent progress in the engineering of
topologically nontrivial phases (such as $\mathbb{Z}_2$ topological insulators,
quantum anomalous Hall effects, quantum valley Hall effects \textit{etc.}) in
two-dimensional material systems, including quantum wells, atomic crystal
layers of elements from group III to group VII, and the transition metal
compounds.
