Until the 1980s, experimental evidence suggested that virtually all solid materials were either amorphous or ordered three-dimensional structures with translational and rotational symmetry that were described by classical crystallographic concepts. Since then, a number of structures that stretch the concept of a crystalline material have been discovered. This book describes the structure and properties of quasicrystalline materials, reviews some of the unique phases that have been observed for elemental carbon, and discusses them in the context of related materials with traditional crystallographic order.