Solvent selection and design are imperative in the CO2 capture process. The efficiency and the overall cost of the process are directly affected by the solvent as a consequence of the effect of solvent on factors such as CO2 absorption capacity, size of equipment, and solvent regeneration energy. This review paper aims to review the most important solvents and mixtures of solvents, absorbing CO2 via chemisorption, physisorption and chemi-physisoprtion. Characteristic and structure of different solvents are presented with the advantages and disadvantages of each being highlighted. Mixtures of solvents include chemical or physical solvents only, and combinations of physical and chemical solvents are categorised. In addition to common solvents, phase change solvents are also described. Once a comprehensive list of solvents is presented, different methods of solvent selection and design are illustrated, namely methods involving experiments, process and equilibrium models, predictive models, and computer-aided molecular design (CAMD). The importance of integrated solvent and process selection and design is also discussed. The most recent and selected progress studies in each section are reviewed in detail. •Role of solvent in CO2 capture is discussed.•The most important solvents and their mixtures are reviewed.•Characteristic, advantages and disadvantages of different solvents are presented.•Different methods of solvent selection and design are illustrated.