This paper reviews the optical properties of ZnO/(Zn, Mg)O single quantum wells grown by molecular beam epitaxy. Both heteroepitaxial quantum well growth along the polar c-direction and homoepitaxial quantum well growth on the nonpolar M plane cases are considered. The optical properties of these quantum wells are investigated by using reflectance, continuous wave photoluminescence, and time-resolved photoluminescence spectroscopies. The quantum-confined Stark effect dominates the properties of

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... the excitons for polar quantum wells. The magnitude of the internal electric field that is induced by both spontaneous and piezoelectric polarizations is determined by comparing the experimental results with a variational calculation of excitonic energies and lifetimes. For nonpolar quantum wells, the optical spectra reveal strong in-plane optical anisotropies, as predicted by the group theory. Moreover, the radiative recombination of free excitons is dominating the quantum well photoluminescence even at room temperature.