Abstract
This paper reviews the current developments in the exciting field of self-assembled semiconductor quantum-dot structures during epitaxial growth of lattice mismatched systems. The formation of quantum-sized islands in the coherent Stranski - Krastanow growth mode, with focus on the possibilities of vertical and lateral ordering, and their electronic properties are described in detail. A overview is given of the self-organizing formation and optical properties of buried (InGa)As quantum discs found in a new growth mode in the metalorganic vapour-phase epitaxy of strained layers on high-index semiconductor surfaces.