The luminescence, luminescence excitation, reflection, and Raman scattering spectra of planar ZnMnTe/ZnMgTe nanostructures with ZnMnTe quantum wells of different widths and elemental composition have been studied. Based on the optical measurements, the energy levels of the nanostructures have been found. It has been shown that the intracenter luminescence excitation spectrum of manganese ions contains a detailed information on the electronic spectrum of the nanostructures. The factors affecting the band widths of exciton luminescence of the quantum wells has been considered. The Raman scattering spectra depends considerably on the parameters of the nanostructure and the relation between the energies of incident photons and intrinsic resonances of the nanostructure.