Polymers of intrinsic microporosity (PIMs) have macromolecular backbones that cannot undergo large-scale conformational changes (i.e. they are “rigid) and that incorporate units that twist them into a coiled conformation (i.e. they are “contorted”). Consequently, they cannot pack efficiently in the solid-state, but possess a high degree of interconnected free volume, leading to high gas permeabilities. Gas permeation data for two PIMs were first reported in 2005 and were shown to surpass the 1991 Robeson upper bound of performance for important gas pairs. Since then, there has been much research on PIMs, leading in 2015 to greatly improved upper bounds for the for O2/N2, H2/N2, and H2/CH4 gas pairs. The archetypal PIM, PIM-1, has been extensively investigated for gas separations. The effects of membrane treatment, membrane thickness, pressure, and feed composition are here considered. Research on the chemical modification of PIM-1 and the effects of chemical, ultraviolet, and thermal cross-linking of PIM-1 are also discussed. Also considered are combinations of PIM-1 with other polymers (polymer blends) and with inorganic, metal–organic, or carbon-based fillers (mixed matrix membranes), as well as new polymers and copolymers prepared using the same dibenzodioxane-forming chemistry as that of PIM-1. Further developments of the PIM concept include polyimides of intrinsic microporosity (PIM-PIs), some of which are thermally rearrangeable and carbonisable, and Tröger’s base (TB) PIMs.