  Majorana zero mode is an exotic quasi-particle excitation with non-Abelian
statistics in topological superconductor systems, and can serve as the
cornerstone for topological quantum computation, a new type of fault-tolerant
quantum computation architecture. This review paper highlights recent progress
in realizing Majorana modes in iron-based high-temperature superconductors. We
begin with the discussion on topological aspect of electronic band structures
in iron-based superconductor compounds. Then we focus on several concrete
proposals for Majorana modes, including the Majorana zero modes inside the
vortex core on the surface of Fe(Te,Se), helical Majorana modes at the hinge of
Fe(Te,Se), the Majorana zero modes at the corner of the Fe(Te,Se)/FeTe
heterostructure or the monolayer Fe(Te,Se) under an in-plane magnetic field. We
also review the current experimental stage and provide the perspective and
outlook for this rapidly developing field.
