Increasing demand to strengthen energy security has increased the importance of natural gas sweetening and biogas upgrading processes. Membrane-based separation of carbon dioxide (CO2) and methane (CH4) is a relatively newer technology, which offers several competitive advantages, such as higher energy-efficiency and cost-effectiveness, over conventional technologies. Recently, the use of graphene-based materials to elevate the performance of polymeric membranes have attracted immense attention. Herein, we do not seek to provide the reader with a comprehensive review of this topic but rather highlight the key challenges and our perspectives going ahead. We approach the topic by evaluating three mainstream membrane designs using graphene-based materials: (1) nanoporous single-layer graphene, (2) few- to multi-layered graphene-based stacked laminates, and (3) mixed-matrix membranes. At present, each design faces different challenges, including low scalability, high production cost, limited performance enhancement, and the lack of robust techno-economic review and systematic membrane design optimization. To help address these challenges, we have mapped out a technology landscape of the current graphene-based membrane research based on the separation performance enhancement, commercial viability, and production cost. Accordingly, we contend that future efforts devoted to advancing graphene-based membranes must be matched by progress in these strategic areas so as to realize practical and commercially relevant graphene-based membranes for CO2/CH4 separation and beyond.