ZnO-based dilute magnetic semiconductors have attracted great interest for their promising application potential in spintronics. Observation of ferromagnetic-like behavior in oxides in general directs the recent focus to defect-rich undoped ZnO thin films and nanostructures. Such magnetic properties are generally mediated by the defects exclusive of magnetic ion doping, thus called defect-induced d0 ferromagnetism (FM). However the intrinsic origin of d0 FM in such materials is controversially reported. In this review we aim to locate the root of the controversy by revisiting the way how the defects were characterized and correlated with the d0 FM in each situation. We found that the main cause of controversy is rooted in a long term debate on the nature of native defects concerning the unintentional n-type conductivity in as-grown ZnO. It is particularly manifested in the assignment of the green luminescence center in photoluminescence spectra and electron paramagnetic resonance signals near g = 1.96 and g = 2.0. Only through X-ray-based microscopy and spectroscopy analysis, can the intrinsic origin of d0 FM in undoped ZnO be unambiguously attributed to the O 2p orbitals arising from zinc vacancies, rather than the Zn 3d orbitals and oxygen vacancies. In spite of the complex defect state in the nanostructures, certain parameters that influence the d0 FM in undoped ZnO systems can be extracted from various reports. Finally, we summarize the challenges and general conclusions on the d0 FM in undoped ZnO nanostructures, followed by outlooks on potential device application in spintronics. It is clear that an important step to promote d0 FM in ZnO for spintronics is to stabilize enough V-zn in ZnO nanostructures, either through acceptor doping or epitaxial growth of strained films, without diminishing the crystalline quality of the structure. Future research focusing on this direction will hopefully produce new breakthrough in device applications. (C) 2017 Elsevier Ltd. All rights reserved.