Ion implantation, specified by parameters like ion energy, ion fluence, ionflux and sub-strate temperature, has become a well-established tool tosynthesize buried low-dimensional nanostructures. In general, in ion beamsynthesis the evolution of nanostructures is determined by the competitionbetween ballistic and thermodynamic effects. A kinetic 3D latticeMonte-Carlo model is introduced, which allows for a proper incorporation ofcollisional mixing and phase separation within supersaturatedsolid-solutions. It is shown, that for both the ballistically andthermodynamically dominated regimes, the Gibbs-Thomson relation is the keyingredient in understanding nanocluster evolution. Various aspects ofprecipitate evolution during implantation, formation of ordered arrays ofnanophase domains by focused ion implantation and compound nanoclustersynthesis are discussed.