Intake and digestibility of feeds by ruminants are influenced by characteristics of the feed, animal and feeding situation. Integration of these characteristics in mathematical models is critical to future progress in forage evaluation and optimal formulation of diets for ruminants. The physiological and physical theories of intake regulation can be described by simple mathematical equations. These equations indicate that intake is a linear function of animal characteristics, such as body weight and production level, and a reciprocal function of feed characteristics, such as fill effect and energy content. Theoretical equations were developed to predict intake when the neutral detergent fiber and energy content of the diet and the energy requirements of the animal are known. The theoretical model also can be used to predict the maximum intake that will maintain a given level of animal production by solving the physiological and physical intake equations at their intersection. Psychogenic intake regulation, which is related to the animal's behavioral response to factors not related to physiological or physical characteristics, can be described mathematically as a multiplier. Digestibility can be predicted by summing the contents of ideal nutritive entities in feeds, which have true digestibilities near 100%, subtracting their associated endogenous losses and adding the variable digestible fiber content. Steady-state models indicate fractional rates of digestion and passage can be used to define ideal nutritive entities and predict digestibility over a range of kinetic characteristics. The steady-state solutions are particularly useful in understanding and predicting the depression in digestibility associated with changes in rates of passage at high levels of feed intake.