Over the past two decades, membrane processes have gained a lot of attention for the separation of gases. They have been found to be very suitable for wide scale applications owing to their reasonable cost, good selectivity and easily engineered modules. This critical review primarily focuses on the various aspects of membrane processes related to the separation of biogas, more in specific CO₂ and H₂S removal from CH₄ and H₂ streams. Considering the limitations of inorganic materials for membranes, the present review will only focus on work done with polymeric materials. An overview on the performance of commercial membranes and lab-made membranes highlighting the problems associated with their applications will be given first. The development studies carried out to enhance the performance of membranes for gas separation will be discussed in the subsequent section. This review has been broadly divided into three sections (i) performance of commercial polymeric membranes (ii) performance of lab-made polymeric membranes and (iii) performance of mixed matrix membranes (MMMs) for gas separations. It will include structural modifications at polymer level, polymer blending, as well as synthesis of mixed matrix membranes, for which addition of silane-coupling agents and selection of suitable fillers will receive special attention. Apart from an overview of the different membrane materials, the study will also highlight the effects of different operating conditions that eventually decide the performance and longevity of membrane applications in gas separations. The discussion will be largely restricted to the studies carried out on polyimide (PI), cellulose acetate (CA), polysulfone (PSf) and polydimethyl siloxane (PDMS) membranes, as these membrane materials have been most widely used for commercial applications. Finally, the most important strategies that would ensure new commercial applications will be discussed (156 references).