The adsorption of H2 in a cross-linked poly(styrene-co- divinylbenzene) (St-DVB) microporous polymer (BET surface area 920 m2 g-1) is studied by volumetric and gravimetric methods, FTIR spectroscopy at variable temperature (300-14 K) and ab initio calculations. At 77 K the polymer reversibly stores up to 1.3 mass% H2 at a pressure of 1 bar and 1.8 mass% at 10 bar. The adsorption process involves the specific interaction of H2 with the structural phenyl rings through weak dispersive forces. The interacting molecules become IR active and give rise to vibrational and rotational-vibrational manifestations which are affected by the temperature, the contact time and the H2 equilibrium pressure. The spectra of the H2/St-DVB system reported here represent the first IR evidence of the adsorption of hydrogen on unsaturated molecules. The adsorption enthalpy is evaluated by the VTIR (variable temperature IR spectroscopy) method (C. Otero Areán et al., Phys. Chem. Chem. Phys., 2007, DOI: 10.1039/b615535a) and compared with the results of ab initio calculations for the H2/benzene interaction and with literature data.