​The field of metal–organic framework based mixed matrix membranes (M⁴s) is critically reviewed, with special emphasis on their application in CO₂ capture during energy generation. After introducing the most relevant parameters affecting membrane performance, we define targets in terms of selectivity and productivity based on existing literature on process design for pre- and post-combustion CO₂ capture. Subsequently, the state of the art in M⁴s is reviewed against these targets. Because final application of these membranes will only be possible if thin separation layers can be produced, the latest advances in the manufacture of M4 hollow fibers are discussed. Finally, the recent efforts in understanding the separation performance of these complex composite materials and future research directions are outlined.