Abstract. Theoretical investigation of electronic and optical properties of selfassembled quantum dots is reviewed. The single particle states of lens-shaped, diskshaped, and vertically coupled dots are discussed. The spectrum of a single exciton, the exciton in the presence of many electrons, and many-exciton complexes are covered. The emission, absorption, far infrared spectroscopy, capacitance, photocurrent spectroscopy and inelastic light scattering as a probe of the ground and excited states of quantum dots charged with electrons and excitons are discussed.