Publisher Summary This chapter discusses the modern state of the theory of diatomic interactions in two comparative ways, one from the energetic and force-theoretical viewpoint, and the other from the mathematical and interpretative viewpoint. These viewpoints have been studied in the framework of two complementary subspaces of the whole phase space of a given diatomic molecule, the position, and the momentum subspaces. Such an approach is useful in the study of the dynamical aspects of diatomic interactions. Some power-series expansion approaches are discussed for the adequate representation of diatomic interaction in the neighborhood of its potential minima in the chapter. The momentum-space aspect of diatomic interactions is also discussed, which provides a new picture complementary to the ordinary picture in position space. The manner of the description of diatomic interactions in the framework of the density functional theory is considered. The chapter basically focuses on the mathematical aspect of the theory of diatomic interactions.