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Microporous organic polymers offer the possibility of storing hydrogen safely at low temperatures and moderate pressures via physisorption. A range of polymers of intrinsic microporosity (PIMs) have been studied. The best PIM to date is based on a triptycene monomer and takes up 2.7% H-2 by mass at 10 bar/77 K. Hypercrosslinked polymers (HCPs) also show promising performance, particularly at pressures > 10 bar. The form of the H-2 isotherm is influenced by the micropore distribution, a higher concentration of ultramicropores (pore size <0.7 nm), as found in PIMs, being associated with enhanced low pressure adsorption. The performance of polymers relative to other microporous materials (carbons and metal-organic frameworks) is compared and promising methods to enhance the hydrogen uptake of microporous polymers are suggested.