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• Choosing a landfill location is a complex process. • Many influential factors must be assessed and evaluated. • The factors could be physical, environmental, social, or economical. • Multi Criteria Decision Making (MCDM) can help the decision making process. • With enough time and resources, Fuzzy Analytical Network Process is most effective. Although a lot of research has focused on energy recovery and recycling of valuable materials from wastes to reduce loads on landfills, landfilling is still an inseparable part of solid waste management. Since landfills potentially pose a risk to human health and the surrounding environment, landfill site selection is an important endeavor that has to be carried out with great care. Choosing a suitable location for landfills depends on several factors and is a complicated procedure. In this paper, a comprehensive review of landfill site selection methods, with an emphasis on multi criteria decision making (multiple criteria decision analysis) has been presented. Assessments indicate that the most frequently used methods are weighted linear combination (WLC), ordered weighted averaging (OWA), analytic hierarchy process (AHP), fuzzy analytic hierarchy process (F-AHP), TODIM, fuzzy TODIM, analytic network process (ANP), fuzzy-analytic network process (F-ANP), and grey systems theory, each of which is discussed. The most widely used factors for selecting a landfill site are groundwater depth, surface water vicinity, elevation, land slope, soil permeability, soil stability, flooding susceptibility, lithology and stratification, faults, land use type, nearby settlements and urbanization, cultural and protected site vicinity, wind direction, roads, railways, proximity to building materials, pipelines and powerlines, and proximity to airports. Image, graphical abstract [ABSTRACT FROM AUTHOR]