Hybrid porous solids, with their tunable structures, their multifunctional properties and their numerous applications, are currently topical, particularly in the domain of adsorption and storage of greenhouse gases. Most of the data reported so far concern the performances of these solids in this domain, particularly in terms of adsorbed amounts of gas but do not explain at the atomic level why and how adsorption and storage occur. From a combination of structural, spectroscopic, thermodynamic experiments and of molecular simulations, this tutorial review proposes answers to these open questions with a special emphasis on CO₂ and CH₄ storage by some rigid and flexible hybrid porous materials.