Membrane technology has gained great attention as one of the promising strategies for carbon capture and separation. Intended for such application, membrane fabrication from various materials has been attempted. While gas separation membranes based on dense polymeric materials have been long developed, there is a growing interest to use porous materials as the membrane material. This review then focuses on emerging organic-containing microporous materials to be used for the fabrication of membranes that are designed for CO2 separation. Criteria for selecting the materials are first discussed, including physical and chemical properties, and parameters in membrane fabrication. Membranes based on these materials, such as metal-organic frameworks, porous organic frameworks, and microporous polymers, are then reviewed. Finally, special attention is given to recent advances, challenges, and perspectives in the development of such membranes for carbon capture and separation. © 2019 Elsevier B.V.