In recent years, there has been increasing interest in ZnO nanostructures due to their variety of morphologies and availability of simple and low cost processing. While there are still unanswered questions concerning fundamental properties of this material, in particular those related to defects and visible luminescence lines, great progress has been made in synthesis methods and device applications of ZnO nanostructures. In this review, we will provide a brief overview of synthesis methods of ZnO nanostructures, with particular focus on the growth of perpendicular arrays of nanorods/nanowires which are of interest for optoelectronic device applications. Then, we will provide an overview of material properties of ZnO nanostructures, issues related to doping with various elements to achieve either p- or n-type conductivity. Doping to alter optical or magnetic properties will also be discussed. Then, issues related to practical problems in achieving good electrical contacts to nanostructures will be presented. Finally, we will provide an overview of applications of ZnO nanostructures to light-emitting devices, photodetectors and solar cells.