We review our recent first-principles results on the inverse Heusler compounds and the ordered quaternary (also known as LiMgPdSn-type) Heusler compounds. Among these two subfamilies of the full-Heusler compounds, several have been shown to be magnetic semiconductors. Such material can find versatile applications, e.g. as spin-filter materials in magnetic tunnel junctions. Finally, a special case are the spin-gapless semiconductors, where the energy gap at the Fermi level for the one spin-direction is almost vanishing, offering novel functionalities in spintronic/magnetoelectronic devices. (C) 2016 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution 3.0 Unported License.