  The discovery of quasicrystals phases and approximants in Al(rich)-Mn system
has revived the interest for complex aluminides containing transition-metal
atoms. On one hand, it is now accepted that the Hume-Rothery stabilization
plays a crucial role. On the other hand, transition-metal atoms have also a
very important effect on their stability and their physical properties. In this
paper, we review studies that unifies the classical Hume-Rothery stabilization
for sp electron phases with the virtual bound state model for transition-metal
atoms embedded in the aluminum matrix. These studies lead to a new theory for
\"spd electron phases\". It is applied successfully to Al(Si)--transition-metal
alloys and it gives a coherent picture of their stability and physical
properties. These works are based on first-principles calculations of the
electronic structure and simplified models, compared to experimental results. A
more detailed review article is published in Prog. Mater. Sci. 50 (2005) p.
679-788.
