The gastrointestinal tract is a complex and intricate machinery to process and absorb nutrients from food in a highly controlled and efficient way. One of the main purposes is to provide essential nutrients (proteins, fats, and carbohydrates) to the blood in a soluble form that can be further processed by the body. For this reason, the food is digested by various enzymes and brought into a state in which it can be absorbed by the small intestines. The proliferation of obesity in the Western world has motivated several research groups to study the digestion process, ultimately to control food intake by food design. This paper reviews the literature related to the digestion of food emulsions, describing in detail the organization and function of the various organs of the gastrointestinal tract, the way these organs cooperate and how this cooperation is regulated by physiological signals. The insight may help to cross the bridge toward designed food structuring from a food-engineering and physical-chemical perspective. Based on the physiological understanding of fat digestion, opportunities to affect the digestion of triglycerides by food structure and composition, stability under stomach conditions, and delayed digestion and absorption in the small intestine are identified.