Ab-initio DFT calculations have been made of native point defects – aluminum vacancies and interstitials and oxygen vacancies and interstitials – and point defect clusters, in both pure sapphire (α-Al2O3) and sapphire doped with the aliovalent solutes Mg and Ti. These calculations have been carried out by and in collaboration with Hine, Frensch, Finnis and Foulkes of Imperial College, London and have resolved the corundum “conundrum” (corundum is the mineral name forα-Al2O3 . The conundrum in question is the “buffering” evident in self-diffusion data of pure and doped crystals and how to interpret the sizeable activation energy found experimentally for oxygen diffusion. Based on these calculations, textbook descriptions of point defects in α-Al2O3 and other ionic materials need revision. Further, migration barriers for diffusion of these point defects have been calculated, permitting robust estimation of the self-diffusion of oxygen and aluminum in pure and doped materials. The calculated diffusivities are in excellent agreement with experiment.