Crystallization kinetics of the three main components of cocoa butter, the triacylglycerols POP, POS, and SOS (where P, O, and S stand for palmitic, oleic, and stearic acids, respectively) were studied by combined differential scanning calorimetry and polarized light microscopy. The morphologies, nucleation kinetics, growth kinetics, and phases of the grains formed were identified with this system. The experimental data, as well as two different models to simulate crystallization and to predict behavior of the pure triacylglycerols, are presented. The first model is based on a macroscopical approach to solidification by using time-temperature-transformation (TTT) diagrams and the additivity principle. It allows prediction of the proportion of the different phases formed for any given thermal path imposed on the sample once the TTT diagram is known for the product. It is illustrated for SOS at constant cooling rates and is compared with experimental results. The second model directly simulates growth of the spherulites in the sample by using nucleation and growth rates that are determined experimentally. II provides a view of the structure as it would be observed with a microscope and shows evolution of the heat released in the sample. Isothermal solidification of POP at 15 degrees C is displayed. The experiment and the model are in good agreement.