In recent years, gas–liquid membrane contactors have attracted increasing attention. A membrane contactor is a device that realizes gas–liquid or liquid–liquid mass transfer without being dispersed in another phase. The membrane gas absorption method combines the advantages of chemical absorption and membrane separation, in addition to exhibiting high selectivity, modularity, and compactness. This paper introduces the operating principle and wetting mechanism of hollow membrane contactors, shows the latest research progress of membrane contactors in gas separation, especially for the removal of carbon dioxide from gas mixtures by membrane contactors, and summarizes the main aspects of membrane materials, absorbents, and membrane contactor structures. Furthermore, recommendations are provided for the existing deficiencies or unsolved problems (such as membrane wetting), and the status and progress of membrane contactors are discussed.