23In this paper, we discuss recent efforts from the last 20 years to describe transport in municipal 24 solid waste (MSW). We first discuss emerging themes in the field to draw the reader's attention to 25 a series of significant challenges. We then examine contributions regarding the modelling of 26 leachate flow to study transport via mechanistic and stochastic approaches, at a variety of scales. 27Since MSW is a multiphase, biogeochemically active porous medium, and with the aim of 28 providing a picture of transport phenomena in a wider context, we then discuss a selection of 29 studies on leachate flow incorporating some of the complex landfill processes (e.g. biodegradation, 30 settlement). It is clear from the literature survey that our understanding of transport phenomena 31 exhibited by landfilled waste is far from complete. Attempts to model transport have largely 32 consisted of applying representative elementary-scale models (the smallest volume which can be 33 considered representative of the entire waste mass). Due to our limited understanding of fluid flow 34 through landfilled waste, and the influence of simultaneously occurring biogeomechanical 35 processes within the waste mass, elementary-scale models have been unable to fully describe the 36 flow behaviour of MSW. Pore-scale modelling and experimental studies have proven to be a 37 promising approach to study fluid flow through complex porous media. Here, we suggest that pore-38 scale modelling and experimental work may provide valuable insights into transport phenomena 39 exhibited by MSW, which could then be used to revise elementary-scale models for improved 40 representation of field-scale problems. 41 42 43 44 4 KEYWORDS 45 municipal solid waste; modelling leachate transport; landfill; waste heterogeneity; preferential 46 flow. 47 6 2000; Rosqvist et al. , 2005) with some studies focusing on conceptual models of the pore structure 89 of MSW at the elementary scale Woodman et al., , 2015 Woodman et al., 90 2013). However, to date, our understanding of the flow of leachate, biogas and the impact of other 91 simultaneously occurring biogeochemical processes on flow and transport is incomplete, 92 especially at the pore-scale. This is particularly important to note since it is these pore-scale 93 processes, with the possibility of field-scale processes dominating particular facets at particular 94 times, that ultimately govern the overall behaviour in reactive porous media (Blunt, 2001; Blunt 95 et al., 2013;Menke et al., 2017;Xiong, 2015;Xiong et al., 2016). It is likely that processes average 96 over a wide range of different scales, which would explain the success of the widely used empirical 97 landfill gas models. The real challenge lies in the integration of modelling processes at all the 98 scales and understanding how averaging works. It is clear that one of the most difficult aspects to 99 model is the inherent heterogeneity of the waste mass, and the impact of different waste 100 components (e.g. their shapes, sizes and varyi...