In a pyrolysis reactor, organic polymers from biomass or plastic waste are thermally decomposed into volatile gases, condensable vapours (tar or bio-oil) and solid residues (char). Since these products may serve as building blocks for downstream chemical refinement or form the basis of bio-derived fuels, pyrolysis is thought to be instrumental in our progress towards a circular economy. A pyrolysis reactor constitutes a multiphase reactive system whose operation is influenced by many chemical and physical phenomena that occur at different scales. Because the interactions and potential reinforcements of these processes are difficult to isolate and elucidate experimentally, the development of a predictive modelling tool, for example, based on the CFD-DEM (discrete element method) methodology, is attracting increasing attention, particularly for pyrolysis reactors operated with biomass as feedstock. By contrast, CFD-DEM descriptions of plastic pyrolysis remain a challenge at present, mainly due to an incomplete understanding of their melting behaviour. In this article, we provide a blueprint for describing a pyrolysis process within the scope of CFD-DEM, review modelling choices made in past investigations and detail the underlying assumptions. Furthermore, the influence of operating conditions and feedstock properties on the key metrics of the process, such as feedstock conversion, product composition and residence time, as determined by past CFD-DEM analyses is surveyed and systematised. Open challenges that we identify pertain to the incorporation of particle non-sphericity and polydispersity, the melting of plastics, particle shrinkage, exothermicity on part of the gas-particle chemistry and catalytic effects.