Membrane technology has emerged as a promising approach for various CO₂ capture applications, including but not limited to hydrogen purification, natural gas processing, biogas upgrading and flue gas post-treatment. Past decades have seen tremendous efforts in developing new materials with better intrinsic separation capacities. However, only a few of them have made their way to the market. It is therefore timely to compile a review that identifies the gap between materials development and fabrication of asymmetric membranes for carbon capture applications. In this review, we give an overview of the recent development of membrane materials for CO₂ separation. Then, we summarize the processing techniques to turn materials into asymmetric membranes and state-of-the-art membranes. Based upon detailed presentation of literature data, we identify the obstacles preventing CO₂ capture membranes from moving from the lab to the large scale. Last, perspectives on future membrane development are discussed.