Mathematical models in fish nutrition have proven indispensable in estimating growth and feed requirements. Nowadays, reducing the environmental footprint and improving product quality of fish culture operations are of increasing interest. This review starts by examining simple models applied to describe/predict fish growth profiles and progresses towards more comprehensive concepts based on bioenergetics and nutrient metabolism. Simple growth models often lack biological interpretation and overlook fundamental properties of fish (e.g. ectothermy, indeterminate growth). In addition, these models disregard possible variations in growth trajectory across life stages. Bioenergetic models have served to predict not only fish growth but also feed requirements and waste outputs from fish culture operations. However, bioenergetics is a concept based on energy-yielding equivalence of chemicals and has significant limitations. Nutrient-based models have been introduced into the fish nutrition literature over the last two decades and stand as a more biologically sound alternative to bioenergetic models. More mechanistic models are required to expand current understanding about growth targets and nutrient utilization for biomass gain. Finally, existing models need to be adapted further to address effectively concerns regarding sustainability, product quality and body traits.