  Intermetallic Heusler alloys are amongst the most attractive half-metallic
systems due to the high Curie temperatures and the structural similarity to the
binary semiconductors. In this review we present an overview of the basic
electronic and magnetic properties of the half-metallic full-Heusler alloys
like Co$_2$MnGe. Ab-initio results suggest that the electronic and magnetic
properties in these compounds are intrinsically related to the appearance of
the minority-spin gap. The total spin magnetic moment in the unit cell, $M_t$,
scales linearly with the number of the valence electrons, $Z_t$, such that
$M_t=Z_t-24$ for the full-Heusler alloys opening the way to engineer new
half-metallic alloys with the desired magnetic properties. Moreover we present
analytical results on the disorder in Co$_2$Cr(Mn)Al(Si) alloys, which is
susceptible to destroy the perfect half-metallicity of the bulk compounds and
thus degrade the performance of devices. Finally we discuss the appearance of
the half-metallic ferrimagnetism due to the creation of Cr(Mn) antisites in
these compounds and the Co-doping in Mn$_2$VAl(Si) alloys which leads to the
fully-compensated half-metallic ferrimagnetism.
