The properties of catenated nitrogen molecules, molecules containing internal chains of bonded nitrogen atoms, is of fundamental scientific interest in chemical structure and bonding, as nitrogen is uniquely situated in the periodic table to form kinetically stable compounds often with chemically stable N-N bonds but which are thermodynamically unstable in that the formation of stable multiply bonded N2 is usually thermodynamically preferable. This unique placement in the periodic table makes catenated nitrogen compounds of interest for development of high-energy-density materials, including explosives for defense and construction purposes, as well as propellants for missile propulsion and for space exploration. This review, designed for a chemical audience, describes foundational subjects, methods, and metrics relevant to the energetic materials community and provides an overview of important classes of catenated nitrogen compounds ranging from theoretical investigation of hypothetical molecules to the practical application of real-world energetic materials. The review is intended to provide detailed chemical insight into the synthesis and decomposition of such materials as well as foundational knowledge of energetic science new to most chemists.