The solution-diffusion model has emerged over the past 20 years as the most widely accepted explanation of transport in dialysis, reverse osmosis, gas permeation, and pervaporation. In this paper we will derive the phenomenological equations for transport in these processes using the solution-diffusion model and starting from the fundamental statement that flux is proportional to a gradient in chemical potential. The direct and indirect evidence for the model's validity will then be presented, together with a brief discussion of the transition between a solution-diffusion membrane and a pore-flow membrane seen in nanofiltration membranes and some gas permeation membranes.