Post-combustion CO2 capture from the flue gas is one of the key technology options to reduce greenhouse gases, because this can be potentially retrofitted to the existing fleet of coal-fired power stations. Adsorption processes using solid sorbents capable of capturing CO2 from flue gas streams have shown many potential advantages, compared to other conventional CO2 capture using aqueous amine solvents. In view of this, in the past few years, several research groups have been involved in the development of new solid sorbents for CO2 capture from flue gas with superior performance and desired economics. A variety of promising sorbents such as activated carbonaceous materials, microporous/mesoporous silica or zeolites, carbonates, and polymeric resins loaded with or without nitrogen functionality for the removal of CO2 from the flue gas streams have been reviewed. Different methods of impregnating functional groups, including grafting techniques and modifying the support materials, have been discussed to enhance the performance of the sorbents. The performance characteristics of the solid sorbents are assessed in terms of various desired attributes, such as their equilibrium adsorption capacity, selectivity, regeneration, multicycle durability, and adsorption/desorption kinetics. The potential of metal-organic frameworks (MOFs) is also recognized to determine whether these novel materials provide better CO2 adsorption capacity under low CO2 partial pressure. A comprehensive critical review and analysis of the literature on this subject has been carried out to update the recent progress in this arena. A comparison of different solid sorbents at different stages is made. It also includes a brief review on techno-economic analysis and design aspects of sorbent bed contactor configuration. Finally, a few recommendations have been proposed for further research efforts to progress post-combustion carbon capture.