The preparation of porous carbons by post-synthesis treatment of hypercrosslinked polymers is described, with a careful physico-chemical characterization, to obtain new materials for gas storage and separation. Different procedures, based on chemical and thermal activations, are considered; they include thermal treatment at 380 °C, and chemical activation with KOH followed by thermal treatment at 750 or 800 °C; the resulting materials are carefully characterized in their structural and textural properties. The thermal treatment at temperature below decomposition (380 °C) maintains the polymer structure, removing the side-products of the polymerization entrapped in the pores and improving the textural properties. On the other hand, the carbonization leads to a different material, enhancing both surface area and total pore volume—the textural properties of the final porous carbons are affected by the activation procedure and by the starting polymer. Different chemical activation methods and temperatures lead to different carbons with BET surface area ranging between 2318 and 2975 m2/g and pore volume up to 1.30 cc/g. The wise choice of the carbonization treatment allows the final textural properties to be finely tuned by increasing either the narrow pore fraction or the micro- and mesoporous volume. High pressure gas adsorption measurements of methane, hydrogen, and carbon dioxide of the most promising material are investigated, and the storage capacity for methane is measured and discussed.