Macronutrients (protein, fats and carbohydrates) are fundamental dietary components, yet the question of what represents a macro-nutritionally balanced diet and how this maintains health and longevity remains unanswered. We have developed a set of state-space models called the Geometric Framework (GF) to capture the multidimensional nature of nutritional requirements, the relative values of foods in relation to these requirements, the behavioural and physiological responses when feeding on diets of varying composition, and the growth and performance consequences of being restricted to particular dietary regimes. We have also derived the necessary theory for defining health and performance in relation to nutrient intake, for describing key nutritional traits and assessing trade-offs between different responses. I begin by introducing these models and then show how they have been used to address problems in life-history theory, appetite, immunity, ageing, obesity, cardio-metabolic health, gut microbial ecology, and foetal development.