While the crystalline state is convenient for describing many properties of real solids, there are a number of important cases where this picture cannot be used, even as a starting point for more elaborate descriptions, as was done for defects in chapters 9–11. As an example, we look at solids in which certain symmetries such as rotations, reflections, or an underlying regular pattern are present, but these symmetries are not compatible with three-dimensional periodicity. Such solids are called quasicrystals. Another example involves solids where the local arrangement of atoms, embodied in the number of neighbors and the preferred bonding distances, has a certain degree of regularity, but there is no long-range order of any type. Such solids are called amorphous. Amorphous solids are very common in nature; glass, based on SiO2, is a familiar example.

In a different class of non-crystalline solids, the presence of local order in bonding leads to large units which underlie the overall structure and determine its properties. In such cases, the local structure is determined by strong covalent interactions, while the variations in large-scale structure are due to other types of interactions (ionic, hydrogen bonding, van der Waals) among the larger units. These types of structures are usually based on carbon, hydrogen and a few other elements, mostly from the first and second rows of the Periodic Table (such as N, O, P, S). This is no accident: carbon is the most versatile element in terms of forming bonds to other elements, including itself.