With the rapid spread in use of polymers the study of diffusion in them is becoming increasingly important. For a number of industrial processes diffusion coefficients and elemental distributions need to be quantified precisely. From a more scientific approach accurate models need to be devised to describe the various diffusion mechanisms involved as well as the concentration and temperature dependencies of the diffusion coefficients. Using ion beam analysis techniques (Rutherford Backscattering and Nuclear Reaction Analysis) three systems were studied. The first was an industrially relevant system of relatively small dye molecules diffusing into a number of different polymer matrices. For fixed diffusion settings, diffusion coefficients were measured and found to correlate with the matrix glass transition temperatures. Surface dye concentrations, on the other hand, were independent of matrix properties. The other two systems studied involved polymer interdiffusion. Based on different assumptions, two contradictory theories have been developed to describe the concentration dependence of the mutual diffusion coefficient; the 'slow' and 'fast' theories. In one system, blends of low molecular weight (unentangled) polystyrene and poly(methyl methacrylate) our data followed the 'slow' theory at low temperatures and the 'fast' theory at high temperatures. An equation describing the concentration dependence of the mutual diffusion coefficient at all intermediate annealing temperatures (hence linking the 'slow' and 'fast' theories) was developed and found to describe the data accurately. In the second system, blends of entangled poly(methyl methacrylate) of several molecular weights, the mutual diffusion coefficient was found to follow the 'fast' theory at all studied temperatures. In all three systems the temperature dependence of the tracer diffusion coefficients of the various components were accurately described by the semi-empirical equations of the Free Volume theory.