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% H2 by mass at 10 bar/77 K. Hypercrosslinked polymers (HCPs) also show promising performance, particularly at pressures >10 bar. The form of the H2 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.