Landfill methane currently represents the largest global source of greenhouse gas emissions from the solid waste sector. Emissions are expected to increase due to increasing waste generation, particularly in countries still landfilling biodegradable wastes. As a complementary measure to gas extraction with subsequent flaring or energy conversion, or for emissions reduction from old landfills or from landfills containing wastes with a low gas potential, microbial methane oxidation systems (MMOS) are considered a promising technology. Numerous studies relating to controlling factors and enhancement of microbial methane oxidation in biocovers, biowindows or biofilters, both in laboratory and in large scale field settings, have been published. The design of optimized MMOS requires thorough understanding of the involved processes, specifically the biological ones and of those related to the transport of gas and water in porous media, and of the impact of material properties and external environmental factors on these processes. Consequently, the selection of materials that are suitable from a biogeochemical and from a geotechnical point of view, meeting the required water and gas transport properties, are key aspects in the design process. This paper reviews the scientific background of the relevant concepts and processes dictating MMOS performance, and provides guidance on layout and design steps, including choice of materials and quality control. Further, a decision tree to support the choice of MMOS is proposed. This paper provides the scientific foundation for upcoming technical guidance documents.