As energy consumption and waste generation from human activities continue to rise, the technology of anaerobic digestion (AD), which converts waste into bioenergy, has gained popularity. Biogas produced from AD commonly contains 60 % CH4, 40 % CO2 and a minor fraction of impurities. Currently, several anaerobic reactors have been designed to upgrade the biogas with biomethane content above 90 %. This review summarizes the current trends in the biological upgradation of biogas from a bio-circular economy perspective to achieve sustainable energy goals. Examples of applications reporting the latest advancements in treating industrial effluents using high-rate anaerobic reactors have been mentioned. The integrated anaerobic-aerobic hybrid reactor offers a solution to the limitations of traditional methods in treating diverse effluents. A special focus on biological upgradation techniques such as in-situ, ex-situ, and hybrid mechanisms have been briefed. The key advantage of hybrid upgradation is its ability to address the pH rise during in-situ process. Additionally, the applications of artificial neural networks and optimization to upgrade biogas production have been discussed. The review concludes with future research directives with emphasis on the economic viability of the approaches.