We review the literature on the use of computational methods to study the reactions between carbon dioxide and aqueous organic amines used to capture CO2 prior to storage, reuse, or sequestration. The focus is largely on the use of high level quantum chemical methods to study these reactions, although the review also summarizes research employing hybrid quantum mechanics/molecular mechanics methods and molecular dynamics. We critically review the effects of basis set size, quantum chemical method, solvent models, and other factors on the accuracy of calculations to provide guidance on the most appropriate methods, the expected performance, method limitations, and future needs and trends. The review also discusses experimental studies of amine-CO2 equilibria, kinetics, measurement and prediction of amine pKa values, and degradation reactions of aqueous organic amines. Computational simulations of carbon capture reaction mechanisms are also comprehensively described, and the relative merits of the zwitterion, termolecular, carbamic acid, and bicarbonate mechanisms are discussed in the context of computational and experimental studies. Computational methods will become an increasingly valuable and complementary adjunct to experiments for understanding mechanisms of amine-CO2 reactions and in the design of more efficient carbon capture agents with acceptable cost and toxicities.