Anaerobic digestion produces biogas, a mixture of CH4 and CO2, where CH4 is a low cost, environmentally friendly, and renewable energy source. The application of biogas production is increasing rapidly as a means of reducing the pollution impact of organic biomasses. However, biogas contains unwanted elements such as hydrogen sulfide, carbon monoxide, siloxanes, and carbon dioxide. To remove these elements, several biogas upgrading technologies like water scrubbing, amine scrubbing, pressure swing adsorption, and membrane separation have been developed and are being used at various commercial scales. Problems with these methods are high energy consumption, the use of expensive chemicals, and high operating cost. Therefore, a major effort is currently underway to improve the design of existing methods as well as developing innovative new upgrading technologies such as cryogenic separation and biological upgrading. This review intends to provide a comprehensive overview of the limitations with the existing upgrading technologies along with recent advances in physical, chemical, and biological biogas upgrading technologies (e.g., pressure swing adsorption, membrane separation, biochar adsorption and CO2 conversion by biological organisms) and further into possible future solutions, such as hybrid systems. Comparative studies of process complexities and associated economic concerns are also provided, and future perspectives that may facilitate research into sustainable biogas upgrading technologies are discussed, focusing in particular on cryogenic separation, novel biological techniques, biochar based upgrading and hybrid technologies incorporating two or more different methods seamlessly integrated. Display omitted •Numerous physical, chemical and biological as well as hybrid methods for upgrading biogas are reviewed.•Many of the upgrading technologies require a high amount of energy and/or costly chemicals needing recovery.•Biological technologies can play a vital role due to lower chemical and energy requirements as well as the production of extra valuable methane form CO2.•Hybrid technologies can potentially be useful and lead to lower cost of upgrading.•Techno-economic analysis and environmental impacts could provide input for a qualified decision between the different processes in the future.