An overview is given of the crystallography of aperiodic crystals, in particular of incommensurately modulated structures and incommensurate intergrowth compounds. The symmetry, the description of the structure and diffraction are described. An extensive discussion is given of crystallographic methods for determination of incommensurate crystal structures. A series of specific compounds is discussed in detail, covering the various ways of incommensurateness. Special attention is given to the commensurate approximation and to the superspace description of superstructures. An historical introduction and a section on the relation between physical properties and incommensurate structure are included.