The urgent need to reduce CO2 emissions is pushing scientists and engineers towards the development of technologies that should prevent further buildup of this greenhouse gas in the atmosphere. Among the technologies under scrutiny, carbon capture and storage (CCS) from large point sources and direct air capture (DAC) are seen as viable options for rapid large scale deployment. The state-of-the-art sorbents for CCS and DAC are typically amine-based: aqueous methanolamine solutions for CCS, solid-supported amine adsorbents for DAC. In both cases, the working principle exploits the formation of covalent bonds between the amine groups and CO2 to afford carbamates (chemical adsorption or chemisorption). The formation of strong covalent bonds is associated with a high heat of absorption or adsorption, which is convenient to achieve high capture loading at low partial pressures, but poses challenges in terms of regeneration of the sorbent and achievable working capacity. While DAC demands a sorbent with a high enthalpy of ab-/adsorption, due to the large entropic loss associated with CO2 capture from a feed that contains only ~415 ppm of CO2, CCS deals with CO2 concentrations in the range between 4 and 30% and could greatly benefit from a sorbent with a mild heat of adsorption, i.e. a physisorbent. To this end, adsorbents such as porous carbons, zeolites and metalorganic frameworks (MOFs) are intensely investigated.