We present a review of current research on the optical properties of ZnO nanostructures. We provide a brief introduction to different fabrication methods for various ZnO nanostructures and some general guidelines on how fabrication parameters (temperature, vapor-phase versus solution-phase deposition, etc.) affect their properties. A detailed discussion of photoluminescence, both in the UV region and in the visible spectral range, is provided. In addition, different gain (excitonic versus electron hole plasma) and feedback (random lasing versus individual nanostructures functioning as Fabry-Perot resonators) mechanisms for achieving stimulated emission are described. The factors affecting the achievement of stimulated emission are discussed, and the results of time-resolved studies of stimulated emission are summarized. Then, results of nonlinear optical studies, such as second-harmonic generation, are presented. Optical properties of doped ZnO nanostructures are also discussed, along with a concluding outlook for research into the optical properties of ZnO.