The success of gas separation processes based on polymeric permselective membranes ultimately depends on the gas transport properties (notably permeability and intrinsic permselectivity) of the polymeric membrane material. (Note that the term “membrane” is used here to denote the thin, compact, permselective layer that controls transport in “asymmetric” or “composite” membrane configurations.) In order to be in a position to design high-performance polymeric membrane materials in a systematic manner, we need some fundamental understanding of the mechanism of gas transport therein and of the main factors that control its rate and selectivity. Our intention here is to present the main lines of theoretical modeling that have been pursued and to discuss the underlying theoretical concepts, rather than to embark on an exhaustive review of individual models and variants thereof.