This article reviews the polymorphism of the principal triacylglycerols (TAGs) in single and binary mixture states. In the first section, the basic concepts of fat polymorphism, namely, thermal stability, subcell structure, and chain‐length structure are explained together with the phase equilibria of binary mixture systems. Then, the polymorphic behavior of the principal TAGs is described. The phase behavior of the mixture systems of the principal TAGs and natural fats is discussed with an emphasis on the influence of the polymorphism.