Hydrogen sulphide (H2S) and volatile methylsiloxanes (VMSs) are key pollutants from the point of view of the operators of biogas plants. H2S poses corrosive hazards, while VMSs transform into difficult-to-remove deposits, reducing the availability and yield of biogas combustion equipment. This study provides a critical overview and evaluation (so-called SWOT analysis) of implemented and promising methods to reduce the content of the above pollutants in biogas, with particular emphasis on biological techniques. The aim of the analyses was to develop an innovative concept for a hybrid biological method for the combined removal of H2S and VMSs using the same device, i.e., a two-phase biotrickling filter (BTF), in which the organic phase that intensifies the mass transfer of VMSs is in the form of a low-viscosity methyl silicone oil. The finally developed technological schematic diagram includes the basic devices and media streams. The concept is characterized by closed media circuits and comprehensively solves the problem of purifying biogas from sewage sludge. In conclusion, key issues requiring further research are identified.