Recent years have seen a large increase in interest in interfaces of ionic and ceramic crystals and an appreciation of their importance in determining many of the properties of materials. Static-lattice calculations have made a major impact on the interpretation of the role of point defects in controlling observed behaviour in the bulk and are now beginning to play a similar role in the study of interfaces. Studies of the free surface are well developed and this paper concentrates on the problems and challenges of the emergent areas of solid–solid interfaces. The first example is of studies of the grain boundaries in nickel oxide. Calculations preceded any detailed experiments of the structure of boundaries in oxides but such studies are now being carried out. The discrepancies between the model and observation are discussed. The second example concerns the interface between an oxide and a metal. Here calculations lag behind experiment because of the need to develop a theoretical appreciation of the nature of the bonding at the interface. Progress towards a satisfactory atomistic model is reviewed.