With global warming becoming one of the main problems our society is facing nowadays, there is an urgent demand to develop materials suitable for CO2 storage as well as for gas separation. Within this context, hierarchical porous structures are of great interest for in-flow applications because of the desirable combination of an extensive internal reactive surface along narrow nanopores with facile molecular transport through broad "highways" leading to and from these pores. Deep eutectic solvents (DESs) have been recently used in the synthesis of carbon monoliths exhibiting a bicontinuous porous structure composed of continuous macroporous channels and a continuous carbon network that contains a certain microporosity and provides considerable surface area. In this work, we have prepared two DESs for the preparation of two hierarchical carbon monoliths with different compositions (e.g., either nitrogen-doped or not) and structure. It is worth noting that DESs played a capital role in the synthesis of hierarchical carbon monoliths not only promoting the spinodal decomposition that governs the formation of the bicontinuous porous structure but also providing the precursors required to tailor the composition and the molecular sieve structure of the resulting carbons. We have studied the performance of these two carbons for CO2, N2, and CH4 adsorption in both monolithic and powdered form. We have also studied the selective adsorption of CO2 versus CH4 in equilibrium and dynamic conditions. We found that these materials combined a high CO2-sorption capacity besides an excellent CO2/N2 and CO2/CH4 selectivity and, interestingly, this performance was preserved when processed in both monolithic and powdered form.