Carbon capture technologies, including absorption, adsorption, and membrane separation, have emerged as one of the research hotspots, in the process of achieving carbon peaking and carbon neutrality goals. Membrane separation, which relies on the difference in gas permeability, offers advantages such as energy saving, high efficiency, ease of operation, and absence of secondary pollution, leading to significant advancements in recent years. Over the past few decades, researchers have reported a variety of different carbon capture membrane materials in the literature with CO_2 separation performance exceeding the Robeson upper bound. However, only a few of these membrane materials have been implemented in industrial processes or are currently under consideration for industrial-scale applications. In fact, many membrane studies have been conducted on a laboratory scale with small membrane areas, resulting in limited information on the practical applicability of membrane separation. This paper combines the industrial CO_2 separation or capture process to introduce the applications of both commercially available membranes and those still under development. It reviews the experimental progress and engineering application cases of membrane separation technology for biogas decarbonization and flue gas carbon capture. Finally, considering the existing challenges, the paper proposes suggestions for the future development direction of membrane separation carbon capture.