The rate-determining process in dry oxidation of silicon for thicker oxides (say above 10 nm) is probably the interstitial diffusion of oxygen molecules. For thinner oxides (a few nm), this simple picture is inadequate. The Deal-Grove model of oxidation kinetics fails. Oxide usually grows by an essentially layer-by-layer process, with growth at terraces, not steps, and perhaps oscillatory roughening. Isotope experiments show that interstitial and network oxygens exchange close to the Si/oxide interface and close to the oxide/gas interface. These results imply limiting mechanisms other than diffusion, probably involving charged oxygen species. We have made Density Functional (DFT) Generalised Gradient Approximation (GGA) calculations for a range of neutral and charged oxygen species to assess relative stabilities, diffusion mechanisms, and propensity for isotope exchange. These results identify acceptable mechanisms. We have also used Monte-Carlo methods to examine the consequences of the image interaction bias, and also the effects of the charge transfer processes (like tunnelling) by which charged species form. We comment on implications for oxide quality, especially on the relationship between growth processes and the charge and energy localisation components of breakdown.