The agriculture and livestock industry generate waste used in anaerobic digestion to produce biogas containing methane (CH4), useful in the generation of electricity and heat. However, although biogas is mainly composed of CH4 (~65%) and CO2 (~34%), among the 1% of other compounds present is hydrogen sulphide (H2S) which deteriorates engines and power generation fuel cells that use biogas, generating a foul smell and contaminating the environment. As a solution to this, anoxic biofiltration, specifically with biotrickling filters (BTFs), stands out in terms of the elimination of H2S as it is cost-effective, efficient, and more environmentally friendly than chemical solutions. Research on the topic is uneven in terms of presenting performance markers, underestimating many microbiological indicators. Research from the last decade was analyzed (2010–2020), demonstrating that only 56% of the reviewed publications did not report microbiological analysis related to sulphur oxidising bacteria (SOB), the most important microbial group in desulphurisation BTFs. This exposes fundamental deficiencies within this type of research and difficulties in comparing performance between research works. In this review, traditional and microbiological performance markers of anoxic biofiltration to remove H2S are described. Additionally, an analysis to assess the efficiency of anoxic BTFs for biogas desulphurisation is proposed in order to have a complete and uniform assessment for research in this field.