The structure of diatomic molecules is discussed in this chapter. The electronic structure of diatomic molecules is then discussed in detail. The coupling of the orbital and spin angular momenta of electrons and the angular momentum associated with nuclear rotation are discussed, with an emphasis on Hund’s cases (a) and (b). The rotational wavefunctions for diatomic molecules in the limits of Hund’s cases (a) and (b) and in the case intermediate between Hund’s cases (a) and (b) are then discussed in detail. For molecules that are of importance in combustion diagnostics, such as OH, CH, CN, and NO, the electronic levels are intermediate between Hund’s cases (a) and (b). We use Hund’s case (a) as the basis wavefunctions, and linear combinations of these wavefunctions are used to represent wavefunctions for electronic levels intermediate between cases (a) and (b). The choice of case (a) wavefunctions as the basis set is typical in the literature although case (b) wavefunctions can also be used as a basis set.