The inelastic scattering of neutrons from adsorbed H2 is an effective and highly sensitive method for obtaining molecular level information on the type and nature of H2 binding sites in porous materials. While these inelastic neutron scattering (INS) spectra of the hindered rotational and translational excitations on the adsorbed H2 contain a significant amount of information, much of this can only be reliably extracted by means of a detailed analysis of the spectra through the utilization of models and theoretical calculations. For instance, the rotational tunneling transitions observed in the INS spectra can be related to a value for the barrier to rotation for the adsorbed H2 with the use of a simple phenomenological model. Since such an analysis is dependent on the model, it is far more desirable to use theoretical methods to compute a potential energy surface (PES), from which the rotational barriers for H2 adsorbed at a particular site can be determined. Rotational energy levels and transitions for the hindered rotor can be obtained by quantum dynamics calculations and compared directly with experiment with an accuracy subject only to the quality of the theoretical PES. In this paper, we review some of the quantum and classical mechanical calculations that have been performed on H2 adsorbed in various porous materials, such as clathrate hydrates, zeolites, and metal-organic frameworks (MOFs). The principal aims of these calculations have been the interpretation of the INS spectra for adsorbed H2 along with the extraction of atomic level details of its interaction with the host. We describe calculations of the PES used for two-dimensional quantum rotation as well as rigorous five-dimensional quantum coupled translation-rotation dynamics, and demonstrate that the combination of INS measurements and computational modeling can provide important and detailed insights into the molecular mechanism of H2 adsorption in porous materials.