The concepts behind some of the more widely used mathematical models of the anaerobic digestion process are described and discussed together with some recent microbiological and biochemical studies that might provide a basis for the next generation of mathematical models. First order rate equations are commonly used for the initial hydrolysis of complex organics and Monod kinetics are widely used to describe methanogenesis from acetate. Depending on circumstances, either of these reactions may be considered as the rate-limiting reaction of the overall fermentation. Thermodynamic calculations provide a valuable tool for modelling intermediate metabolism but the metabolic repertoire of these bacteria still provides a few surprises for the fermentation chemist. A possible new concept for modelling patterns of volatile fatty acids during overload and recovery of anaerobic digesters is described and discussed.