This chapter reviews the polymorphism of principal triacylglycerols in single and binary mixture states. First, basic concepts of fat polymorphism, namely, thermal stability, subcell structure and chain length structure are explained together with phase equilibria of binary mixture systems. Then, polymorphic behavior of principal triacylglycerols are described. The phase behavior of the mixture systems of the principal TAGs is discussed with an emphasis of the influence of the polymorphism.