This work presents a critical review on the recent developments in the design and optimization of efficient post-combustion CO2 capture processes from point sources, focusing on absorption, adsorption, and membrane separations. Emphasis is placed on the efficient modeling and simulation frameworks, synthesis and design studies, and model-based optimization approaches. Furthermore, the interactions between material (solvent, adsorbent, membrane) development and process design and optimization, are explored. Comparison among the different carbon capture processes, shows that absorption is still the most mature technology for post-combustion CO2 capture. Amines are the most appropriate solvents for CO2 absorption, although significant amount of energy is required for solvent regeneration. On the other hand, the development of materials used in adsorption and membrane-based separations has not reached a mature level that can lead to efficient CO2 capture, employing simple process configurations. Consequently, more complex configurations and design specifications are necessary in these processes, which usually result in an increased separation cost.