Self-propagating reactions in free-standing multilayer foils provide a unique opportunity to study very rapid, diffusion-based transformations in non-equilibrium material systems. To fully understand the coupling between mass and thermal diffusion controlling these reactions and to optimize the commercial use of reactive foils, we have undertaken analytical and numerical modeling. Our analytical model predicts an increase in the reaction velocities with decreasing bilayer thickness down to a critical bilayer thickness and a reversal in this trend below the critical thickness. Predicting reaction characteristics such as the flame thermal width, the reaction zone width and the effect of variations in material properties with temperature has proven analytically intractable. To overcome these limitations, we have also used numerical methods to determine the composition and temperature profiles ahead of the reaction front for different multilayer periods and premixing. The results are compared with experimental values where possible.