Observations of the motion of ions by means of both diffusion and electrical conductivity measurements usually show deviations from the normal Einstein relation. The interpretation of these deviations often leads to a fairly detailed picture of the types of defects present and the mechanisms of their motion. A correction must always be considered because of the fact that successive jumps of a tracer atom are correlated, as first discussed by Bardeen and Herring, and the origin of this effect is shown by treating diffusion as a random walk problem. For the interstitialcy mechanism a second correction is required because the effective displacement is larger for conductivity than diffusion, and this effect is illustrated with results on AgCl and AgBr. Possible mechanisms for ionic motion in crystals with the CsCl structure are described, and the present interpretation of results for CsBr, CsI, and TlCl is discussed. It appears that vacancy pairs may make an appreciable contribution to the diffusion. Experiments for observing diffusion with an applied electric field are discussed, and an analysis is given of the problem of determining the internal electric field in such situations. If certain experimental difficulties can be overcome, this last technique should provide a powerful extension of methods of investigating the motion of ions in crystals.