Raw biogas generated in the anaerobic digestion (AD) process contains several undesired constituents such as H2S, CO2, NH3, siloxanes and VOCs. These gases affect the direct application of biogas, and are a prime concern in biogas utilization processes. Conventional physico-chemical biogas purification methods are energy-intensive and expensive. To promote sustainable development and environmental friendly technologies, biological biogas purification technologies can be applied. This review describes biological technologies for both upstream and downstream processing in terms of pollutant removal mechanisms and efficiency, bioreactor configurations and different operating conditions. Limitations of the biological approaches and their future scope are also highlighted. A conceptual framework Driver-Pressure-Stress-Impact-Response (DPSIR) and Strengths-Weaknesses-Opportunities-Threats (SWOT) analysis have been applied to analyse the present situation and future scope of biological biogas clean-up technologies.