Carbon dioxide emissions must be stabilized to mitigate the unfettered release of greenhouse gases into the atmosphere. The removal of carbon dioxide from flue gases, an important first step in addressing the problem of CO2 emissions, can be achieved through adsorption separation technologies. In most adsorption processes, the adsorbent is in contact with fluid in a fixed bed. Fixed-bed column mathematical models are required to predict the performance of the adsorptive separation of carbon dioxide for optimizing design and operating conditions. A comprehensive mathematical model consists of coupled partial differential equations distributed over time and space that describe material, energy, and the momentum balances together with transport rates and equilibrium equations. Due to the complexities associated with the solution of a coupled stiff partial differential equation system, the use of accurate and efficient simplified models is desirable to decrease the required computational time. The simplified model is primarily established based on the description of mass transfer within adsorption systems. This paper presents a review of efforts over the last three decades toward mathematical modeling of the fixed-bed adsorption of carbon dioxide. The nature of various gas-solid equilibrium relationships as well as different descriptions of the mass transfer mechanisms within the adsorbent particle are reviewed. In addition to mass transfer, other aspects of adsorption in a fixed bed, such as heat and momentum transfer, are also studied. Both single- and multi-component CO2 adsorption systems are discussed in the review. (C) 2013 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.