A critical review is given on self-diffusion, impurity diffusion, chemical diffusion, thermal diffusion and radiation-enhanced diffusion in the ceramic nuclear fuels, i.e. oxides, carbides, nitrides and carbonitrides of uranium and plutonium. Atomic transport in ThO2 is also discussed. Besides experimental results on diffusion, calculations of defect energies, diffusion mechanisms, and the relevant data on kinetic processes related to diffusion, ranging from creep, grain growth and sintering to leaching in water are also treated. Furthermore, recent results on damage-induced defects and their thermal behaviour using ion implantation of UO2 and UN with fission products and Rutherford backscattering/channelling techniques are reported and used to discuss the fission product behaviour in these fuels. Finally, suggestions are made for future work.