After briefly reviewing the current crystallographic theories/models for solid-solid phase transformations, the most recent edge-to-edge matching (E2EM) model will be discussed. The development of the E2EM model was based on the principles that the nature of a coherent or semi-coherent interface and the associated crystallographic relationships are governed by minimization of interfacial energy between two crystals; and that the necessary and sufficient condition for minimization of the interfacial energy is to maximize the atom matching. Major advantage of the E2EM model over all other previous models is its predictive capacity from the first principle. Thus, it can be used to design new alloys and processes. In this presentation, its success in development of new and more effective grain refiners for cast metals, including magnesium alloys, zinc alloys and steels , and for additively manufactured Ti64 alloy is discussed.