What are we trying to simulate?; Digestive enzyme activities in pigs and poultry; The role of the microflora in digestion; The physical and chemical constitution of foods: effects on carbohydrate digestion; Indirect effects of foods antinutrients on protein digestibility and nutritional value of diets; In vitro simulation of digestion and absorptionin the gastro-intestinal tract of pigs and poultry - methods and results; The chemical and biological bases of a calculation system developed for predicting dietary energy values: a poultry model; Enzyme modelling of protein digestion and L-lysine availability; Use of pepsin digentibility, multienzyme pH change and protein solubility assays to predict in vivo protein quality of feedstuffs; Estimation of true ileal digestibility of amino acids with pigs by an in vitro method using intestinal fluid; prediction of the energy value of non-ruminant feeds using in vitro digestion with intestinal fluid and other chemical methods; A model for feed evaluation based on in vitro digestible dry matter and protein; In vitro simulation of protein digestion: an integrated approach; Simultaneous estimations of precaecal protein and carbohydrate digestion in the pig; The way forward; the future requirements of the feed industry; The scientific challenge.