This chapter discusses permeability of polymers to gases and vapors. The objective of this chapter is to complement and update the compilations of gas permeability data. The chapter also includes a brief review of the permeation mechanisms as well as a mention of the use of computer simulations of gas permeation in and through nonporous polymer membranes. The dependence of permeability, diffusion, and solubility coefficients on penetrant gas pressure (or concentration in polymers) is very different at temperatures above and below the glass transition temperature, Tg, of the polymers, i.e., for rubbery and glassy polymers, respectively. By contrast, the permeability, diffusion, and solubility coefficients for gases in glassy polymers are strongly nonlinear functions of the penetrant gas pressure. When the concentration of penetrant gases in glassy polymers becomes sufficiently high to plasticize the polymers, the permeability, diffusion, and solubility coefficients will deviate from dual-mode sorption behavior and increase as the pressure is raised. The chapter contains tables, which list references to many recent and some earlier permeability measurements made with various pure gases and membranes cast from different classes of rubbery and glassy polymers, but mainly homopolymers. The polymers listed here are polyolefins, vinyl polymers and vinylidene polymers, natural and synthetic rubber, polyesters and polycarbonates, cellulose and cellulose derivatives, fluoropolymers, polyorganosiloxanes, polynitriles, polyamides, polyimides, polyurethanes, polyoxides, polysulfones, polyacetylenes and polyacrylics. The ranges of experimental pressure and temperature reported in these references are also listed. Various gas permeability units and their conversion factors are also listed.