The bonding forces and atomic sizes determine the arrangement of the atoms in equilibrium in crystals. The crystal structure is determined by the tendency to fill a given space with the maximum number of atoms under the constraint of bonding forces and atomic radii. Crystal bonding and crystal structure are thus intimately related to each other and determine the intrinsic properties of semiconductors. Nonequilibrium states can be frozen-in and determine the structure of amorphous semiconductors. In an amorphous structure the short-range order is much like that in a crystal, while long-range periodicity does not exist. Quasicrystals are solids with an order between crystalline and amorphous. These quasiperiodic crystals have no three-dimensional translational periodicity, but exhibit long-range order in a diffraction experiment. A quasicrystalline pattern continuously fills all available space; unlike regular crystals space filling requires an aperiodic repetition of (at least) two different unit cells.Superlattices and low-dimensional structures like quantum wires and quantum dots, created by alternating thin depositions of different semiconductors, show material properties which can be engineered by designing size and chemical composition. This opens the feasibility for fabricating new and improved devices.