  We review recent progress in the explorations of topological quantum states
of matter in iron-based superconductors. In particular, we focus on the
nontrivial topology existing in the band structures and superconducting states
of iron's 3d orbitals. The basic concepts, models, materials and experimental
results are reviewed. The natural integration between topology and
high-temperature superconductivity in iron-based superconductors provides great
opportunities to study topological superconductivity and Majorana modes at high
temperature.
