One-dimensional ZnO nanostructures (nanowires/nanorods) are attractive materials for applications such as gas sensors, biosensors, solar cells, and photocatalysts. This is due to the relatively easy production process of these kinds of nanostructures with excellent charge carrier transport properties and high crystalline quality. In this work, we review the photoluminescence (PL) properties of single and collective ZnO nanowires and nanorods. As different growth techniques were obtained for the presented samples, a brief review of two popular growth methods, vapor-liquid-solid (VLS) and hydrothermal, is shown. Then, a discussion of the emission process and characteristics of the near-band edge excitonic emission (NBE) and deep-level emission (DLE) bands is presented. Their respective contribution to the total emission of the nanostructure is discussed using the spatial information distribution obtained by scanning transmission electron microscopy−cathodoluminescence (STEM-CL) measurements. Also, the influence of surface effects on the photoluminescence of ZnO nanowires, as well as the temperature dependence, is briefly discussed for both ultraviolet and visible emissions. Finally, we present a discussion of the size reduction effects of the two main photoluminescent bands of ZnO. For a wide emission (near ultra-violet and visible), which has sometimes been attributed to different origins, we present a summary of the different native point defects or trap centers in ZnO as a cause for the different deep-level emission bands.