The increase in the amount of municipal solid waste (MSW) generated, among other places, in households is a result of the growing population, economic development, as well as the urbanisation of areas with accompanying insufficiently effective measures to minimise waste generation. There are many methods for treating municipal waste, with the common goal of minimising environmental degradation and maximising resource recovery. Biodegradable waste, including selectively collected biowaste (BW), also plays an essential role in the concept of the circular economy (CE), which maximises the proportion of waste that can be returned to the system through organic recycling and energy recovery. Methane fermentation is a waste treatment process that is an excellent fit for the CE, both technically, economically, and environmentally. This study aims to analyse and evaluate the problem of odour nuisance in municipal waste biogas plants (MWBPs) and the impact of the feedstock (organic fraction of MSW-OFMSW and BW) on this nuisance in the context of CE assumptions. A literature review on the subject was carried out, including the results of our own studies, showing the odour nuisance and emissions from MWBPs processing both mixed MSW and selectively collected BW. The odour nuisance of MWBPs varies greatly. Odour problems should be considered regarding particular stages of the technological line. They are especially seen at the stages of waste storage, fermentation preparation, and digestate dewatering. At examined Polish MWBPs cod ranged from 4 to 78 ou/m3 for fermentation preparation and from 8 to 448 ou/m3 for digestate dewatering. The conclusions drawn from the literature review indicate both the difficulties and benefits that can be expected with the change in the operation of MWBPs because of the implementation of CE principles.