In recent years, significant progress has been achieved in developing the potential of anaerobic membrane bioreactors (AnMBRs). The present paper presents a comprehensive review of studies focused on biogas production via the treatment of municipal and domestic wastewater with the use of such technology. The main aim of the current work was to evaluate the impact of operating parameters on the biogas production yield. Moreover, the possibilities of applying various fouling mitigation strategies have been discussed in detail. Analyses have been performed and reported in the literature, which were conducted with the use of submerged and external AnMBRs equipped with both polymeric and ceramic membranes. It has been shown that, so far, the impact of the hydraulic retention time (HRT) on biogas yield is ambiguous. This finding indicates that future studies on this issue are required. In addition, it was demonstrated that temperature has a positive impact on process performance. However, as presented in the literature, investigations have been carried out mainly under psychrophilic and mesophilic conditions. Hence, performing further experimental studies at temperatures above 40 °C is highly recommended. Moreover, it has been shown that in order to restore the initial permeate flux, a combination of several membrane cleaning methods is often required. The findings presented in the current study may be particularly important for the determination of operating conditions and suitable fouling mitigation strategies for laboratory-scale and pilot-scale AnMBRs used for biogas production via the treatment of municipal and domestic conditions.