This paper reviews the structure of the modern theory of atomic transport in solids. It starts with the macroscopic equations of non-equilibrium thermodynamics and then proceeds to the methods offered by statistical mechanics for the evaluation of transport coefficients, etc. The application of these methods to stochastic models is then considered in both general terms and for particular models suggested by the theory of lattice imperfections. These particular examples include isothermal diffusion in dilute and concentrated solid solutions and also transport in temperature gradients. The value of solid state theory in the parameterization of these models is emphasised.