Typically, anodic oxidation of metals results in the formation of hexagonally arranged nanoporous or nanotubular oxide, with a specific oxidation state of the transition metal. Recently, the majority of transition metals have been anodized; however, the formation of copper oxides by electrochemical oxidation is yet unexplored and offers numerous, unique properties and applications. Nanowires formed by copper electrochemical oxidation are crystalline and composed of cuprous (CuO) or cupric oxide (Cu₂O), bringing varied physical and chemical properties to the nanostructured morphology and different band gaps: 1.44 and 2.22 eV, respectively. According to its Pourbaix (potential-pH) diagram, the passivity of copper occurs at ambient and alkaline pH. In order to grow oxide nanostructures on copper, alkaline electrolytes like NaOH and KOH are used. To date, no systemic study has yet been reported on the influence of the operating conditions, such as the type of electrolyte, its temperature, and applied potential, on the morphology of the grown nanostructures. However, the numerous reports gathered in this paper will provide a certain view on the matter. After passivation, the formed nanostructures can be also post-treated. Post-treatments employ calcinations or chemical reactions, including the chemical reduction of the grown oxides. Nanostructures made of CuO or Cu₂O have a broad range of potential applications. On one hand, with the use of surface morphology, the wetting contact angle is tuned. On the other hand, the chemical composition (pure Cu₂O) and high surface area make such materials attractive for renewable energy harvesting, including water splitting. While compared to other fabrication techniques, self-organized anodization is a facile, easy to scale-up, time-efficient approach, providing high-aspect ratio one-dimensional (1D) nanostructures. Despite these advantages, there are still numerous challenges that have to be faced, including the strict control of the chemical composition and morphology of the grown nanostructures, their uniformity, and understanding the mechanism of their growth.