Quasicrystals are metallic alloys, often containing 60 to 70 atomic per cent AI. They typically exhibit crystallographically-forbidden symmetry, such as a fivefold rotational symmetry, illustrated in Fig. 1. Quasicrystals are reasonably abundant in a metallurgical context, since they can be formed by more than 100 combinations of elements. Several of these forms are thermodynamically stable, and knowledge of their phase equilibria is crucial to many aspects of applications. Quasicrystals can be very well-ordered, based upon data from both real- and reciprocal-space techniques.These facts contradict common misperceptions that they are glass-like and exclusively metastable.