Discussion of electronic properties of quasicrystals

Abstract\n This article gives a short review of some important achievements in the field of electronic properties of quasicrystals. It focuses essentially on : the nature of quasicrystals as Hume-Rothery alloys, the energetics of quasicrystals and related phases, the magnetic properties, the localization of electronic states, the transport properties. For each part one emphasizes some promising directions of research. We end by listing some problems that are related to that of electrons in a quasiperiodic potential.