Abstract Hydrogen adsorption in two different metal–organic frameworks (MOFs), MOF‐5 and Cu‐BTC (BTC: benzene‐1,3,5‐tricarboxylate), with Zn 2+ and Cu 2+ as central metal ions, respectively, is investigated at temperatures ranging from 77 K to room temperature. The process responsible for hydrogen storage in these MOFs is pure physical adsorption with a heat of adsorption of approximately –4 kJ mol –1 . With a saturation value of 5.1 wt.‐% for the hydrogen uptake at high pressures and 77 K, MOF‐5 shows the highest storage capacity ever reported for crystalline microporous materials. However, at low pressures Cu‐BTC shows a higher hydrogen uptake than MOF‐5, making Cu‐based MOFs more promising candidates for potential storage materials. Furthermore, the hydrogen uptake is correlated with the specific surface area for crystalline microporous materials, as shown for MOFs and zeolites.