We have established a new concept for creating ordered arrays of quantum dots by self-organized epitaxy. The concept is based on self-organized anisotropic strain engineering of strained layer templates and is demonstrated for (In,Ga)As/GaAs superlattice structures on GaAs (100) and strain-induced (In,Ga)As growth instability on GaAs (311)B. The well-defined one- and two-dimensional networks of InAs quantum dots grown on top of these templates are of excellent structural and optical quality. This breakthrough, thus, allows for novel fundamental studies and device operation principles based on single and multiple carrier- and photon-, and coherent quantum interference effects.