The principles and a quantitative theory of growth for monogastric livestock animals are described here, focusing on the period from birth to slaughter. The theory helps to understand key relationships between the outcomes that may be desired in a production system and their influencing factors, e.g. nutritional, genetic, and environmental, and forms the basis of current mechanistic models for predicting animal performance. We describe general physical, chemical and biological principles that should underlie any description of animal growth; and address growth as a three-faceted problem: 1) growth under 'normal' conditions; 2) growth under 'limiting' conditions; and 3) recovery growth when 'normal' conditions are restored. We propose a theoretical framework that incorporates these situations as facets of a whole, that encompasses growth conditions across modern livestock production systems, and in which terms such as 'normal' and 'limiting' acquire a meaning. To make this framework quantitative, we apply a body of theoretical and empirical principles in the derivation of mathematical models of growth. The usefulness of existing theories and mathematical models depends on the availability of data for testing hypotheses and parameterising models under a range of conditions. A challenge ahead, therefore, is in obtaining extensive data for further testing and consolidating modelling prediction of growth under a wide range of conditions, or as animals respond to change in limitations. Another challenge lies in addressing practical problems posed by heterogeneity in performance within groups of animals: i.e., how to manage groups towards optimal resource use and performance, and how to identify best phenotypical characteristics within breeds, strains, etc. and predict their performance. Further progress will require much greater availability of rich individual data cross-sectioning herds and breeds.