The growth of strained nanocrystals producing self-assembled quantum dots (QDs) and wires (QWRs) has produced convincing examples of low-dimensional behavior. Moreover, the growth of InAs on GaAs (001) in particular has been shown to produce not only interesting examples of fundamental science but also of technologically relevant applications, mainly in the area of laser research. It is then of utmost importance the investigation of the growth processes in strained epitaxy, involving both thermodynamic and kinetic pathways to the production of such systems.Here the focus is on the thermodynamic aspects of nanocrystal growth, choosing as a model system the epitaxial growth of Ge : Si (001). This is an interesting system to build the knowledge of nanocrystal growth, giving the reduced number of experimental parameters one has. With the lessons learned from this system, InAs : GaAs (001) QDs were grown near thermal equilibrium, generating a reproducible and uniform ensemble of nanocrystals. In a different regime, the growth of self-organized rare-earth silicide wires can be achieved upon proper choice of growth temperature and growth rate. These few examples show that the subtleties of strained nanocrystal growth can be explored in such a way that by knowing the thermodynamics and kinetics of a particular material system many interesting low-dimensional structures can be created.