A review devoted to the theory of excitonic quasimolecules (Biexcitons) (formed of spatially separated electrons and holes) in a nanosystems that consists of semiconductor and dielectric quantum dots synthesized in a dielectric matrix. It is shown that exciton quasimolecules formation is of the threshold character and possible in nanosystems, in with the spacing between the quantum dots surfaces is larger than a certain critical spacing. It was found that the binding energy of singlet ground state of exciton quasimolecules, consisting of two semiconductor quantum dots is a significant large values, larger than the binding energy of the biexciton in a semiconductor single crystal almost two orders of magnitude.