Membrane processes have been initially seldom considered within a post-combustion carbon dioxide capture framework. More traditional processes, particularly gas-liquid absorption in chemical solvents, are often considered as the most appropriate solution for the first generation of technologies. In this paper, a critical state of the art of gas separation membranes for CO2 capture is proposed. In a first step, the key performances (selectivity, permeability) of different membrane materials such as polymers, inorganic membranes, hybrid matrices and liquid membranes, including recently reported results, are reviewed. In a second step, the process design characteristics of a single stage membrane unit are studied. Purity and energy constraints are analysed as a function of operating conditions and membrane materials performances. The interest of multistage and hybrid systems, two domains which have not sufficiently investigated up to now, are finally discussed. The importance of technico-economical analyses is highlighted in order to better estimate the optimal role of membranes for CCS applications.