Understanding of metal oxidation is critical to corrosion control, catalysis synthesis, and advanced materials engineering. Although, metal oxidation process is rather complicated, different processes, many of them coupled, are involved from the onset of reaction. Since first introduced, there has been great success in applying heteroepitaxial theory to the oxide growth on a metal surface as demonstrated in the Cu oxidation experiments. In this paper, we review the recent progress in experimental findings on Cu oxidation as well as the advances in the theoretical simulations of the Cu oxidation process. We focus on the effects of defects such as step edges, present on realistic metal surfaces, on the oxide growth dynamics. We show that the surface steps can change the mass transport of both Cu and O atoms during oxide growth, and ultimately lead to the formation of different oxide morphology. We also review the oxidation of Cu alloys and explore the effect of a secondary element to the oxide growth on a Cu surface. From the review of the work on Cu oxidation, we demonstrate the correlation of theoretical simulations at multiple scales with various experimental techniques. (C) 2016 Elsevier B.V. All rights reserved.