Aluminum based alloys which contain transition metal elements with concentrations up to 25% and additional small quantities of silicon, have a wide variety of atomic structures with unusual physical properties. Among these materials are the famous quasiperiodic alloys which were discovered in 1984 in Al-Mn by Shechtman et al. One find also numerous complex phases which atomic structures bear resemblance with medium-range structure of quasicrystalline phases. Some of these complex phases, but not all of them, are crystalline approximants of quasicrystals. This review focuses on the effect of the transition metal elements on the electronic structure of these alloys. The case of AI(Si)-Mn alloys is considered as a benchmarking one for the present study. But many of the results and concepts developed here can still be applied to other Al-rich alloys containing TM atom from the 3d, 4d, and 5d series. On the one hand, it is now well accepted that the Hume-Rothery stabilization of the valence electrons plays a crucial role in these materials. On the other hand, it has been shown that the TM atoms are also very important for their stability and their physical properties. But, until recently, there has been no model taking into account these two aspects together. We present a model that unifies the classical Hume-Rothery stabilization for sp electron metals with the virtual bound state model for TM atoms embedded in a metallic matrix. This new formalism for "spd electron phases" is applied successfully to Al(Si)-TM alloys and it gives a coherent conceptual picture of their stability and physical properties. It is compared to accurate first-principles calculations of the electronic structure for these alloys, and to the most important experimental and theoretical results in the literature. We also investigate the transition metal aluminide alloys with a non-metallic character. This can be due either to the creation of a gap or to the localization of electrons by some atomic clusters. Again in that case, the scattering of sp states by d orbitals of transition metal plays a central role. (c) 2005 Elsevier Ltd. All rights reserved.