Lateral ordering of semiconductor quantum dots (QDs) of high quality in well-defined arrangements is essential for the realization of future quantum functional devices with applications in solid state quantum computing and quantum communication [1]. We have developed a new concept for the creation of laterally ordered QD arrays by self-organized epitaxy. The concept is based on self-organized anisotropic strain engineering of (In,Ga)As/GaAs superlattice (SL) templates by molecular beam epitaxy (MBE) and the lateral ordering of (In,Ga)As QDs by local strain recognition. It is demonstrated for one-dimensional (1D) and two-dimensional (2D) QD arrays on planar GaAs (100) [2] and (311)B [3] substrates. Starting from a nanoscale, random (In,Ga)As...