  Ternary semiconducting or metallic half-Heusler compounds with an atomic
composition 1:1:1 are widely studied for their flexible electronic properties
and functionalities. Recently, a new material property of half-Heusler
compounds was predicted based on electronic structure calculations: the
topological insulator. In topological insulators, the metallic surface states
are protected from impurity backscattering due to spin-momentum locking. This
opens up new perspectives in engineering multifunctional materials. In this
article, we introduce half Heusler materials from the crystallographic and
electronic structure point of view. We present an effective model Hamiltonian
from which the topological state can be derived, notably from a non-trivial
inverted band structure. We discuss general implications of the inverted band
structure with a focus on the detection of the topological surface states in
experiments by reviewing several exemplary materials. Special attention is
given to superconducting half-Heusler materials, which have attracted ample
attention as a platform for non-centrosymmetric and topological
superconductivity.
