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We review recent progress in the explorations of topological quantum statesof matter in iron-based superconductors. In particular, we focus on thenontrivial topology existing in the band structures and superconducting statesof iron's 3d orbitals. The basic concepts, models, materials and experimentalresults are reviewed. The natural integration between topology andhigh-temperature superconductivity in iron-based superconductors provides greatopportunities to study topological superconductivity and Majorana modes at hightemperature.

Topological quantum states of matter in iron-based superconductors: From concepts to material realization