Polyazoles and polyazines are, respectively, five‐ and six‐membered nitrogen heterocycles. An interesting difference between their geometries is that it is possible in polyazoles (but not in polyazines) to distinguish between formal single and formal double bonds. Our particular focus in this chapter is on those polyazoles and polyazines that feature three or more linked nitrogens in their rings (nitrogen catenation). The presence of ring nitrogens is destabilizing, especially when they are linked. Several possible factors that may be responsible for this effect of catenation are discussed in detail, and it is emphasized that these factors are not mutually exclusive or independent of each other. The electrostatic potentials of the molecules of interest are analyzed and related to their relative stabilities. N‐oxide formation is one means of mitigating the destabilization caused by nitrogen catenation. The acidity/basicity of these polyazoles and polyazines is examined in terms of their electrostatic potentials and local ionization energies. Polyazoles and polyazines have been found to provide good molecular frameworks for energetic materials; this application is briefly mentioned.