Mathematical modelling as applied to growing pigs and lactating sows is a structured method for deriving quantitative estimates of the productive performance of the animal under varying diets and other conditions. A simple overview is that a model starts with a clear quantitative description of the animal (usually including body protein and fat content), estimates daily protein and fat accretion, updates the description, and repeats those estimates and updates until the desired end-point is reached. This is conceptually simple, but in practice it is quite challenging.A recent book edited by Moughan et al. (1995) provides a thorough description of modelling as applied to the pig. Progress in modelling the pig continues, as shown by recent publication of a model of digestion in the pig (Bastianelli et al. 1996).Models that predict whole-animal performance can vary in the level of aggregation at which they operate. Some models work at the metabolic level, predicting the flows of C and N through metabolic pathways. They do not work at the level of individual reactions, but aggregate those individual reactions into pathways. Others work at the level of lean and adipose tissues, predicting the rates of accretion of protein and fat in these tissues. They thus aggregate all the metabolic transactions into simple expressions of protein and fat accretion, so they are more highly aggregated than are the metabolic models. Still others operate at the whole-animal level, and are the most highly aggregated of all. They often are built of regression equations relating body-weight gain to variables such as dietary lysine concentration or stocking density, and thus aggregate accretion of protein, fat, water, ash, and gut contents into whole-body growth. They are considered empirical models because they are based entirely on observations, with no considerations of the underlying mechanisms. Nutrient-partitioning and metabolic models are considered mechanistic, because they are structured to reflect our perceptions of the mechanisms of animal growth. They admittedly contain empirical elements, because in some areas (e.g. relationship between backfat thickness and body fat content) we have no useful concepts of the underlying mechanisms. The terms empirical and mechanistic as applied to models are relative, not absolute, so there are degrees of mechanism. Metabolic models are more mechanistic than are nutrient-partitioning models, because there is a greater separation between the level of the outputs (whole-animal) and the level at which they are built than in the case of nutrient-partitioning models.Empirical models can be very accurate within the range of conditions in which they were developed, but are unreliable when used in other conditions. Mechanistic models are more reliable over a wider range of conditions because they are built on biological mechanisms. Therefore, they are usually more useful. However, as models become more mechanistic, reliable quantitative estimates of model variables are often more difficult to obtain,...