  This review elaborates pedagogically on the fundamental concept, basic
theory, expected properties, and materials realizations of topological
superconductors. The relation between topological superconductivity and
Majorana fermions are explained, and the difference between dispersive Majorana
fermions and a localized Majorana zero mode is emphasized. A variety of routes
to topological superconductivity are explained with an emphasis on the roles of
spin-orbit coupling. Present experimental situations and possible signatures of
topological superconductivity are summarized with an emphasis on intrinsic
topological superconductors.

Superconductivity