Organocyclic compounds and their ring-opening reactions have been widely exploited in the development of important synthetic polymers and materials for numerous applications. However, although three-membered O-heterocycles, i.e., epoxides, have been used as key components in many functional materials ranging from traditional epoxy resins and hardeners to dielectric insulators and functional nanocomposites, relatively little research has been conducted on their analogous three-membered N-heterocyclic counterparts, i.e., aziridines, in polymer science and technology. Therefore, this article reviews recent achievements in aziridine-based polymer chemistry and presents a brief discussion on the future direction, particularly focusing on polyaddition, post-modification, and cross-linking based on aziridine chemistry.