One important application of polymer/graphene nanocomposites is in membrane technology. In this context, promising polymer/graphene nanocomposites have been developed and applied in the production of high-performance membranes. This review basically highlights the designs, properties, and use of polymer/graphene nanocomposite membranes in the field of gas separation and purification. Various polymer matrices (polysulfone, poly(dimethylsiloxane), poly(methyl methacrylate), polyimide, etc.), have been reinforced with graphene to develop nanocomposite membranes. Various facile strategies, such as solution casting, phase separation, infiltration, self-assembly, etc., have been employed in the design of gas separation polymer/graphene nanocomposite membranes. The inclusion of graphene in polymeric membranes affects their morphology, physical properties, gas permeability, selectivity, and separation processes. Furthermore, the final membrane properties are affected by the nanofiller content, modification, dispersion, and processing conditions. Moreover, the development of polymer/graphene nanofibrous membranes has introduced novelty in the field of gas separation membranes. These high-performance membranes have the potential to overcome challenges arising from gas separation conditions. Hence, this overview provides up-to-date coverage of advances in polymer/graphene nanocomposite membranes, especially for gas separation applications. The separation processes of polymer/graphene nanocomposite membranes (in parting gases) are dependent upon variations in the structural design and processing techniques used. Current challenges and future opportunities related to polymer/graphene nanocomposite membranes are also discussed.