The development of industry is accompanied by large-scale emissions of carbon dioxide (CO2). Carbon capture technologies have become one of the research hotspots in the process of achieving carbon peaking and carbon neutrality goals. Currently, carbon capture technologies mainly involve absorption, adsorption, and membrane separation. Membrane separation relies on differences in gas permeability and offers advantages such as energy savings, high efficiency, ease of operation, and no secondary pollution. It has rapidly developed as a CO2 capture technology in recent years. This paper provides a systematic review of recent advances in biogas and flue gas CO2 capture using membrane separation technology.  It elaborates on CO2 transport mechanisms through membranes, including solution-diffusion, facilitated transport, and molecular sieving. A comparative analysis is conducted on the performance characteristics and suitable application scenarios of three types of membrane materials: polymeric membranes, inorganic membranes, and mixed matrix membranes. For engineering applications, the article consolidates numerous pilot and industrial cases from both domestic and international sources. In biogas decarbonization, membrane separation enables CH₄ purity exceeding 97% and CO2 recovery above 90%. Following distillation, CO2 purity reaches 99.9%, allowing the purified CO2 to be used in the food industry. Regarding flue gas CO2 capture, single- or multi-stage membrane processes elevate CO2 concentration from approximately 15% to 60–95%, with capture rates reaching 80%–90%. Techno-economic analyses suggest a capture cost of USD 40–45 per ton when CO2 purity exceeds 95%. Despite significant progress in membrane technology, several challenges remain, including inadequate resistance to plasticization and aging of membrane materials, difficulty in simultaneously achieving high purity and high capture rates, and the adverse effects of impurities in actual flue gas. Future work must focus on developing membrane materials with enhanced stability and selectivity, optimizing multi-stage membrane integration processes, and promoting the coupling of membrane technology with adsorption and cryogenic separation methods. Efforts should also be strengthened in anti-fouling design and cost control to improve economic efficiency, operational reliability, and environmental adaptability of CO2 capture systems. These advancements will facilitate the large-scale application of membrane separation technology in carbon capture projects.