In review, deals with the theory of exciton quasimolecules (formed of spatially separated electrons and holes) in a nanosystems that consists of semiconductor and dielectric colloidal quantum dots (QDs) synthesized in a dielectric and semiconductor matrixs. It has been shown that the exciton quasimolecule formation is of the threshold character and possible in a nanosystem, where the distance D between the surfaces of QD is given by the condition (where and are some critical distance). We have shown that in such a nanoheterostructures acting as “exciton molecules” are the QDs with excitons localizing over their surfaces. The position of the quasimolecule state energy band depends both on the mean radius of the QDs, and the distance between their surfaces, which enables one to purposefully control it by varying these parameters of the nanostructure. It was found that the binding energy of singlet ground state of exciton quasimolecules, consisting of two semiconductor and dielectric QDs is a significant large values, larger than the binding energy of the biexciton in a semiconductor and dielectric single crystals almost two orders of magnitude. It is shown that the major contribution to tue binding energy of singlet ground state of exciton quasimolecule is made by the energy of the exchange interaction of electrons with holes and this contribution is much more substantial than the contribution of the energy of the Coulomb interaction between the electrons and holes. It is established that the position of the exciton quasimolecule energy band depends both on the mean radius of the QDs and the distance between their surfaces. It is shown that with increase in temperature above the threshold (), a transition can occur from the exciton quasimolecule to exciton state. It has been found that at a constant concentration of excitons (i.e. constant concentration of QD) and temperatures Т below , one can expect a new luminescence band shifted from the exciton band by the value of the exciton quasimolecule binding energy. This new band disappears at higher temperatures (). At a constant temperature below , an increase in exciton concentration (i.e. in QD concentration) brings about weakening of the exciton luminescence band and strengthening of the exciton quasimolecule. These exciton quasimolecules are of fundamental interest as new quasi-atomic colloidal nanostructures; they may also have practical value as new nanomaterials for nanooptoelectronics. The fact that the energy of the ground state singlet exciton quasimolecule is in the infrared range of the spectrum, presumably, allow the use of a quasimolecule to create new infrared sensors in biomedical research.