First-principle calculations, especially by the density functional theory (DFT), is used to study the structure and properties of oxygen/metal interfaces. Adsorption of oxygen molecules or atoms on metal surfaces plays a key role in surface science and technology. This review is dedicated to the adsorption of oxygen molecules or atoms on metal surfaces and diffusion behavior from first-principle investigation. We hope that this review can provide some useful contributions to understand the study of adsorption properties and diffusion behavior on a metal surface at an atomic-scale, especially for those interested in catalytic oxidation and application of corrosion.