Aiming at meeting the global goals established for carbon dioxide (CO₂) reduction, carbon capture and storage (CCS) plays a key role. In this framework, the adsorption-based CO₂ post-combustion capture is considered one of the most promising approaches because it can provide remarkable energy savings with respect to the standard amine-based absorption capture. To date, most of the research effort has been devoted to the development of novel cutting-edge adsorbent materials with the primary purpose of enhancing the adsorption capacity and lifetime while reducing the heat of adsorption, thus lessening the energetic requirement of the sorbent regeneration. Anyway, other factors, beyond the sorbents, greatly affect the competitiveness of the CO₂ capture based on the adsorption route, namely, the gas–solid contacting system, impacting the sorbent utilization efficiency, and the regeneration strategies, determining most of the global CO₂ capture costs. This review describes the state-of-the-art and most recent progresses of the adsorption-based CO₂ post-combustion capture. In particular, the first section describes the CO₂ adsorption performances of different classes of solid sorbents on the basis of the most important evaluation parameters (equilibrium adsorption capacity, multi-cyclic stability, etc.). In the second section, the two main gas–solid contacting systems, i.e., fixed beds and fluidized beds, have been reviewed, pointing out their strengths and limitations. Finally, the third section provides a review on the different regeneration modes (temperature, pressure, or hybrid swings), with a focus on the possible strategies available to limit the energy penalty.