The oxidation and corrosion of metals are fundamental problems in materials science and technology that have been studied using a large variety of experimental and computational techniques. Here we review some of the recent studies that have led to significant advances in our atomic-level understanding of copper oxide, one of the most studied and better understood metal oxides. We show that a good atomistic understanding of the physical characteristics of cuprous (Cu 2 O) and cupric (CuO) oxide and of some key processes of their formation has been obtained. Indeed, the growth of the oxide has been proven to be epitaxial with the surface and to proceed, in most cases, through the formation of oxide nano-islands which, with continuous oxygen exposure, grow and eventually coalesce. We also show how electronic structure calculations have become increasingly useful in helping to characterise the structures and energetics of various Cu oxide surfaces. However a number of challenges remain. For example, it is not clear under which conditions the oxidation of copper in air at room temperature (known as native oxidation) leads to the formation of a cuprous oxide film only, or also of a cupric overlayer. Moreover, the atomistic details of the nucleation of the oxide islands are still unknown. We close our review with a perspective on future work and discuss how recent advances in experimental techniques, bringing greater temporal and spatial resolution, along with improvements in the accuracy, realism and timescales achievable with computational approaches make it possible for these questions to be answered in the near future.