Carbon capture and storage has declined in prominence as a large scale response to climate change, but carbon dioxide capture will remain important into the future for the hydrogen economy, for steel and cement, as well as chemical production. Membrane technology can be a significant component of this industry if cost competitive. While most scientific research is focussed on developing novel materials for this application, it is the process design of the membrane operations that is much more critical in reducing these costs. In post combustion capture, this involves optimisation of the pressure driving force across the membrane, either through feed compression or permeate vacuum pumping, integration of downstream cryogenic purification and the use of combustion air sweeps. In pre-combustion capture, integration of the membrane into the water gas shift reactor is key. Membrane contactors can also play a role, but must be carefully engineered to ensure pressure drop control and to minimise capillary condensation of water.