Atomic diffusion processes in UO2 and in the fast-breeder reactor fuel, (U, Pu)O2 are reviewed. Emphasis is given to the slower-moving species. i.e. U and Pu. Self-diffusion, chemical diffusion, diffusion in a thermal gradient, enhancement of diffusion by radiation and fission and the operative diffusion mechanisms are discussed. The main parameter, besides the temperature, is the oxygen-to-metal ratio (O/M ratio) of the oxide. The experimental results are compared with recent calculations reported elsewhere in this volume. Also treated are effects of the possible λ-transition at ca. 2600 K in UO2 on high-temperature kinetic processes. The present knowledge on the diffusion and mobility of fission products with emphasis on volatile and gaseous elements, and of other actinides with emphasis on their valence states are treated. Gaps in our knowledge are pointed out and the relevance of the available results for oxide fuel during reactor operation is discussed. Whereas much is known for the as-produced ‘virgin’ fuel, more results are urgently needed for oxides with higher burn-ups containing a few per cent fission products. Finally, technological applications of the diffusion results are treated. As an example, important savings in cost, energy and time in fuel sintering were recently achieved based on basic studies of diffusion properties of UO2.