Membrane technology is characterized by high efficiency, compatibility and flexibility of various membrane processes in integrated systems, low power consumption, high stability and environmental safety of processes, comparative ease and simplicity of controlling and scaling-up, as well as a unique functional flexibility of the membrane processes. This is why the membrane technology is considered as a promising way to reduce anthropogenic emissions of carbon dioxide into the atmosphere. Gas-liquid membrane contactors are a prime example of high-performance hybrid processes using membrane technologies. Integrating several separation methods in one device (membrane contactor) makes it possible to retain benefits of membrane technology, such as small size and flexibility, complementing them with high separation selectivity typical of CO2 absorption. This review presents the basic principles of operation and design of membrane contactors, and a wide range of materials, membranes, and liquid absorbents for membrane CO2 absorption/stripping are considered. Particular attention has been paid to current studies on CO2 removal from thermal power plant flue gas, natural gas, biogas, and syngas. The examples of pilot-scale and semi-commercial implementation of CO2 absorption/stripping in membrane contactors have been given.