Since the initial discovery of crystal-like individual arrays of atoms that are not regularly repeated, made in 1982 by Dan Shechtman, the acceptance of the concept and the word quasicrystal have led the International Union of Crystallography to redefine the term crystal to mean "any solid having an essentially discrete diffraction diagram", thereby shifting the essential attribute of crystallinity from position space to Fourier space. Within the family of crystals one distinguishes between traditional crystals, which are periodic, or repeating, at the atomic scale, and aperiodic (incommensurate) crystals which are not. This broader definition adopted in 1996 reflects the current understanding that microscopic periodicity is a sufficient but not a necessary condition for crystals.

While the term "crystal" has a precise meaning within materials science and solid-state physics, colloquially "crystal" refers to solid objects that exhibit well-defined and often pleasing geometric shapes. In this sense of the word, many types of crystals are found in nature. The shape of these crystals is dependent on the types of molecular bonds between the atoms to determine the structure, as well as on the conditions under which they formed. Snowflakes, diamonds, and table salt are common examples of crystals.

Some crystalline materials may exhibit special electrical properties such as the ferroelectric effect or the piezoelectric effect. Additionally, light passing through a crystal is often refracted or bent in different directions, producing an array of colors; crystal optics is the study of these effects. In periodic dielectric structures a range of unique optical properties can be expected as seen in photonic crystals.