The first commercial hollow fiber and flat sheet gas separation membranes were produced in the late 1970s from the glassy polymers polysulfone and poly(vinyltrimethyl silane), respectively, and the first industrial application was hydrogen recovery from ammonia purge gas in the ammonia synthesis loop. Membranes based on glassy polymers (polysulfone, cellulose acetate, polyimides, substituted polycarbonate, and poly(phenylene oxide)) are currently used in various industrial processes, such as hydrogen purification, nitrogen production, and natural gas treatment. However, the glassy polymers are in a non-equilibrium state; therefore, these polymers undergo a process of physical aging, which is accompanied by the spontaneous reduction of free volume and gas permeability over time. The high free volume glassy polymers, such as poly(1-trimethylgermyl-1-propyne), polymers of intrinsic microporosity PIMs, and fluoropolymers Teflon®AF and Hyflon®AD, undergo significant physical aging. Herein, we outline the latest progress in the field of increasing durability and mitigating the physical aging of glassy polymer membrane materials and thin-film composite membranes for gas separation. Special attention is paid to such approaches as the addition of porous nanoparticles (via mixed matrix membranes), polymer crosslinking, and a combination of crosslinking and addition of nanoparticles.