Despite all the work conducted over many decades, there remains a major problem in understanding diffusion in alumina. It is certain that all measurements of diffusion in alumina refer to extrinsic diffusion. However, the experimental activation energy is larger than any theoretical prediction by a factor of 2. The problem with grain boundary diffusion is, if anything, worse. The most complete set of experimental data suggests that the activation energy for boundary diffusion is 50% larger than for bulk diffusion. We discuss the problems involved in understanding the experimental data and in producing theoretical models and propose a strategy for resolving the problems.