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, and for steel and cement as well as chemical production. Membrane technology can be a significant component of this industry if it is cost competitive. While most scientific research is focused 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 postcombustion capture, this involves optimization 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 precombustion capture, integration of the membrane into the steam reformer or 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 minimize capillary condensation of water.