This book introduces the reader to the quantum theories needed to describe the interactions of diatomic molecules with electromagnetic fields and systematically discusses the effects of static and dynamic electric and magnetic fields on the rotational, fine, and hyperfine structure of molecules. It illustrates how the concepts developed in ultracold physics research have lead to what may be the beginning of controlled chemistry in the fully quantum regime. The theories described are applied to discuss examples from research on trapping molecules in electromagnetic fields, laser control of molecular rotations and external field control of microscopic intermolecular interactions. The book presents the description of scattering theory for molecules in electromagnetic fields and is written to be a practical guide for students working on various aspects of molecular interactions.