The gas–liquid membrane contactor technology, which integrates the absorption process with membranes, is a developing membrane technology that is especially pertinent to acid gas absorption. When it comes to removing acid gases from natural gas or after combustion, membrane technology has demonstrated potential as a substitute for conventional absorption columns. The membrane contactor offers exceptional operating flexibility and a high mass transfer area. In addition to summarizing the key elements of membrane materials, absorbents, and membrane contactor design, this paper presents the working principle and wetting mechanism of hollow membrane contactors and focuses the most recent advancements in membrane contactor research in gas separation from gas mixtures. The state-of-the-art overview of highly hydrophobic microporous membranes is presented after a discussion of the main challenges to the preparation of superhydrophobic membranes.