The recent results of development and application of MBE methods for direct growth (self-organization or spontaneous formation) of the heterostructures GexSi1-x/Si are discussed. The heterostructures involve nanoobjects confined in two-or three-dimensional quantum-sized boxes or wires. The influence of substrate temperature, film composition and thickness on the structure and the surface morphology of the growing film were studied. Particular attention was paid to the surface structure evolution of GexSi1-x heteroepitaxial films growing on Si(111)7 X 7 and Si(001)2 X 1 substrates over a wide range of concentrations x and growth temperatures. The quantum-sized islands can be self-organized after achievement of the critical thickness of the pseudomorphic layer; the critical thickness can be calculated in terms of the Frank-van der Merwe theory (when the Stranski-Krastanov growth mechanism is achieved). It was shown that with respect to the electronic properties, such films demonstrate the behavior of quantum boxes in which a zero-dimensional electron (hole) gas is localized. A number of heteroepitaxial structures with Ge quantum boxes in a tunnel-thin Si layers are grown by MBE and investigated.