Thermogravimetric analysis (TGA) is the most widespread thermal analytical technique applied to waste materials. By way of critical review, we establish a theoretical framework for the use of TGA under non-isothermal conditions for compositional analysis of waste-derived fuels from municipal solid waste (MSW) (solid recovered fuel (SRF), or refuse-derived fuel (RDF)). Thermal behaviour of SRF/RDF is described as a complex mixture of several components at multiple levels (including an assembly of prevalent waste items, materials, and chemical compounds); and, operating conditions applied to TGA experiments of SRF/RDF are summarised. SRF/RDF mainly contains cellulose, hemicellulose, lignin, polyethylene, polypropylene, and polyethylene terephthalate. Polyvinyl chloride is also used in simulated samples, for its high chlorine content. We discuss the main limitations for TGA-based compositional analysis of SRF/RDF, due to inherently heterogeneous composition of MSW at multiple levels, overlapping degradation areas, and potential interaction effects among waste components and cross-contamination. Optimal generic TGA settings are highlighted (inert atmosphere and low heating rate (⩽10°C), sufficient temperature range for material degradation (⩾750°C), and representative amount of test portion). There is high potential to develop TGA-based composition identification and wider quality assurance and control methods using advanced thermo-analytical techniques (e.g. TGA with evolved gas analysis), coupled with statistical data analytics.