First-principles quantum techniques based on density functional theory (DFT) have made important contributions to the understanding of oxide surfaces over the last four years. Important features of these calculations include: the use of periodic boundary conditions, which avoid the edge effects associated with the cluster approach; plane-wave basis sets, which make the calculation of ionic forces straightforward, so that both static relaxation and dynamical simulation can be done; and the approximate inclusion of electron correlation. A short introduction to DFT techniques is given, and recent work on the structure and energetics of a variety of oxide surfaces is presented. It is shown how the techniques can be used to study molecular and dissociative adsorption of molecules on oxide surfaces, with the emphasis on water and simple organic molecules. The growing importance of dynamical first-principles simulation in the study of surface chemical reactions is illustrated.