Many recent advances in microelectronics would not have been possible without the development of strain induced nanodevices and bandgap engineering, in particular concerning the common SiGe system. In this context, a huge amount of literature has been devoted to the growth and self-organization of strained nanostructures. However, even if an overall picture has been drawn out, the confrontation between theories and experiments is still, under various aspects, not fully satisfactory. The objective of this review is to present a state-of-the-art of theoretical concepts and experimental results on the spontaneous formation and self-organization of SiGe quantum dots on silicon substrates. The goal is to give a comprehensive overview of the main experimental results on the growth and long time evolution of these dots together with their morphological, structural and compositional properties. We also aim at describing the basis of the commonly used thermodynamic and kinetic models and their recent refinements. The review covers the thermodynamic theory for different levels of elastic strain, but focuses also on the growth dynamics of SiGe quantum dots in several experimental circumstances. The strain driven kinetically promoted instability, which is the main form of instability encountered in the epitaxy of SiGe nanostructures at low strain, is described. Recent developments on its continuum description based on a non-linear analysis particularly useful for studying self-organization and coarsening are described together with other theoretical frameworks. The kinetic evolution of the elastic relaxation, island morphology and film composition are also extensively addressed. Theoretical issues concerning the formation of ordered island arrays on a pre-patterned substrate, which is governed both by equilibrium ordering and kinetically-controlled ordering, are also reported in connection with the experimental results for the fabrication technology of ordered arrays of SiGe quantum dots. (C) 2012 Elsevier B.V. All rights reserved.