Abstract:Half-metallic Heusler alloys are amongst the most promising materials for future magneto-electronic applications. We review some recent results on the electronic properties of these compounds. The origin of the gap in these half-metallic alloys and its connection to the magnetic properties are well understood. Changing the lattice parameter slightly shifts the Fermi level. Spin-orbit coupling induces states within the gap but the alloys keep a very high degree of spin polarization at the Fermi level. Small degrees of doping and disorder as well as defects with low formation energy have little effect on the properties of the gap, while temperature effects can lead to a quick loss of half-metallicity. Finally, we discuss two special issues: the case of quaternary Heusler alloys and the half-metallic ferrimagnets.