In general, the post-combustion capture of CO2 is costly; however, swing adsorption processes can reduce these costs under certain conditions. This review highlights the issues related to adsorption-based processes for the capture of CO2 from flue gas. In particular, we consider studies that investigate CO2 adsorbents for vacuum swing or temperature swing adsorption processes. Zeolites, carbon molecular sieves, metal organic frameworks, microporous polymers, and amine-modified sorbents are relevant for such processes. The large-volume gas flows in the gas flue stacks of power plants limit the possibilities of using regular swing adsorption processes, whose cycles are relatively slow. The structuring of CO2 adsorbents is crucial for the rapid swing cycles needed to capture CO2 at large point sources. We review the literature on such structured CO2 adsorbents. Impurities may impact the function of the sorbents, and could affect the overall thermodynamics of power plants, when combined with carbon capture and storage. The heat integration of the adsorption-driven processes with the power plant is crucial in ensuring the economy of the capture of CO2, and impacts the design of both the adsorbents and the processes. The development of adsorbents with high capacity, high selectivity, rapid uptake, easy recycling, and suitable thermal and mechanical properties is a challenging task. These tasks call for interdisciplinary studies addressing this delicate optimization process, including integration with the overall thermodynamics of power plants. © 2012 Elsevier Ltd.