  Predicting quasicrystal structures is a multifaceted problem that can involve
predicting a previously unknown phase, predicting the structure of an
experimentally observed phase, or predicting the thermodynamic stability of a
given structure. We survey the history and current state of these prediction
efforts with a focus on methods that have improved our understanding of the
structure and stability of known metallic quasicrystal phases. Advances in the
structural modeling of quasicrystals, along with first principles total energy
calculation and statistical mechanical methods that enable the calculation of
quasicrystal thermodynamic stability, are illustrated by means of cited
examples of recent work.
