Membranes are widely used with industrial purposes in the separation of gases, as barriers to protect inside matter from outside environment in both food packaging and beverage bottling, and for coating of cables and electronic components.The gas transport characteristics depends on their physical state (glassy, rubbery, semicrystalline). In this article the classical theory of gas permeation is reviewed Special emphasis is given to the influence of the physical state of the membranes on both the solubility and diffusion coefficients. The influence of the chemical structure and temperature on the permselectivity of membranes is discussed. Finally, attention is also paid to the usefulness of molecular dynamics to predict the diffusional properties of membranes.