The standard definitions and methods of measuring diffusion coefficients in solids are briefly reviewed. Assumptions underlying the simple formulae which have been proposed to relate diffusion coefficients measured by different methods are critically discussed in the light of experimental evidence and theoretical considerations which suggest that modification may be necessary. Difficulties in the way of deciding between several alternative mechanisms for diffusion, and of fully understanding how measured diffusion coefficients are related to the atomic jumps constituting diffusion, are formulated.