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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.