Composting is a valuable method to treat and valorize organic waste. However, the process is defined by its dynamic nature and governed by a multitude of operating parameters. As such, mathematical modelling of the process offers a powerful tool to simulate and predict the variable outcomes of the process, allowing for its optimization. This can include improving efficiency, lowering costs and reducing environmental impact. To aid with the development of future models, we provide an up to date review and assessment on the state of the art of composting modelling. By reviewing 40 years of literature, this review paints the most complete picture of the field to date. This includes an analysis of trends in composting modelling: looking at the type of systems that are targeted, the aim of the models and the approaches to kinetics and mass and heat transfer. Regarding modelling approaches, we explore the fractionation of both substrates and microorganisms, the biological processes that can be included (disintegration, hydrolysis, uptake and death) and their kinetics (first-order, Monod-type), energy balances (biological generation, convection, conduction) and mass balances. We also provide a review of the results of sensitivity analyses performed on composting models, finding that models are most sensitive to microbial growth and death rates, as well as consumption rates and product yields. In the final portion of the review, we identify, explore, and provide guiding recommendations for work on emerging areas and areas requiring development in composting modelling (volume change, pH, maturation, artificial intelligence, etc.)