Abstract
About 50 years ago, it was shown that there are solid state systems with perfect order but without lattice periodicity. These systems were called crystalline phases because of the order and incommensurate because of the lack of periodicity. They formed a challenge for crystallographers and physicists to understand the structure, the physical properties and the reason for their appearance. Later other classes of this type were found (occupation modulated crystals, incommensurate magnetic systems, incommensurate composites), the most important one being that of quasicrystals. The discovery of the latter class in 1982 caused a huge increase in interest. The first conferences on this new type of materials were called Modulated Crystals, later polytypes and quasicrystals were included in the title MOSPOQ. Nowadays these conferences continue under the name Aperiodic (Crystals). The field has become very active worldwide, and our insight into structure and properties has increased impressively. A brief sketch of the development of the field is given in this chapter.
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