Increasing concentration of greenhouse gases in the atmosphere, most notably carbon dioxide (CO₂) has become a global concern as a major cause of climate change and global warming. In order to mitigate such problem, numerous concepts and technologies to reduce CO₂ emission have been developed. Membrane-based technologies have been drawing a great attention for carbon capture applications due to their advantages such as low cost, low energy, flexible in operation, and modularity. The membrane can also be integrated with another process (for example liquid absorption), combining the benefit of both processes such as in the case of membrane contactor (MC). In this work, the recent development of membrane-based carbon capture technologies is reviewed, including membrane gas separation (MGS) and membrane gas absorption or MC. Furthermore, the state of the art and the present status of MGS and MC in carbon capture will be discussed in detail, focusing on the development and challenges for MGS and MC in carbon capture applications. The development of superhydrophobic membrane which is an emerging approach to avoid wetting phenomenon in MC is also discussed. In addition, comparison of MGS and MC performance is also highlighted in this paper. Finally, prospect and challenges of membrane-based carbon capture technology are pointed out.