Technical Abstract: Cost and value of the carcass are fundamental to the economics of livestock production for meat. Feed efficiency and carcass lean and fat composition are biological aspects of the growing animal that show genetic variability. These traits are closely linked to cost and value of the carcass. Unfortunately, understanding feed efficiency and the lean and fat composition of carcasses and their relation to the genotype is difficult because they change dynamically with time. Because these traits are dynamic, models of efficiency and carcass composition have several uses in animal breeding. Models have been used to adjust data, determine selection objectives, suggest selection criteria, and extend results of experiments. Models are especially helpful when carcass value is not linearly related to individual traits. Use of a model to determine the suitability of different cattle genotypes for different markets and optimal slaughter weights under different management is illustrated. Future developments using dynamical systems approaches, simplified carcass trait models, and knowledge of genes and their physiological effects could make predictions more reliable.