We report optical properties of quantum dots and quantum wires of diluted magnetic semiconductors. The quantum dots of Cd1-xMnxSe (x=0.03) show the exciton luminescence at around 2.4 eV, which indicates a strong confinement effect of the exciton energy corresponding to the dot size of 4–6 nm. The Zeeman shift of the exciton luminescence was observed with an effective g value of 91, showing a significant exchange interaction of the excitons with the Mn ions in the dots. The exciton luminescence from the quantum wires of Cd1-xMnxSe (x=0.08) shifts by 5.2 meV to the higher energy side with decreasing the wire width from 126 to 26 nm. The high energy shift in the narrow wires indicates the influence of the one-dimensional quantum confinement effect for the exciton states. The effective g value of the exciton in these quantum wires is 100–150. The exciton luminescence from the wires is linearly polarized (up to 80%) parallel to the wire direction at zero field, which indicates one-dimensional properties of the quantum wire excitons. © 2000 American Institute of Physics.