Results of investigations into surface processes of the formation of germanium and silicon nanostructures are analyzed. A mechanism of three-dimensional island nucleation and relaxation of strained two-dimensional layers in heteroepitaxy of germanium on silicon, which initiates spontaneous island growth, is considered. The oxidation of the silicon surface prior to germanium or silicon deposition drastically alters the growth mechanism, leading to the formation of islands with an extremely high areal density of 10¹²-10¹³ cm^-2 and with sizes of less than 10 nm. The effects of spatial quantization determine their properties. Moreover, arrays of these islands form a unique surface for the growth of Si layers that are able to emit photons in the 1.5-1.6-μm wavelength range.