For one-dimensional nanomaterials, the performances are strongly related to the diameters, lengths, morphologies, and structures, implying that it is of great significance to understand the related growth mechanisms and thus to achieve the desired nanostructures. Thermal oxidation of copper has been widely used to fabricate CuO nanowires (NWs), whereas the growth mechanism still remains controversial in spite of the extensive investigations. Therefore, this review aims to offer a critical discussion about the growth mechanisms. First, the effects of different growth conditions on the growth of CuO NWs are introduced for basic understanding. Subsequently, the proposed mechanisms in different literature studies, i.e., the vapor–solid, self-catalyzed growth, stress-induced growth, stress grain boundary (GB) diffusion, and oxygen concentration gradient, are discussed and summarized. It seems that the combination of “stress GB diffusion” and “oxygen concentration gradient” mechanisms could be relevant for the growth of CuO NWs via thermal oxidation of copper.