[3+2] Annulations are a powerful method for the synthesis of five-membered heterocyclic compounds. The annulations have concerted cycloaddition and formal (stepwise) cycloaddition reaction pathways. In addition to the well-established O-centered and N-centered ylides, epoxides and aziridines could serve as synthetic equivalent of 1,3-dipoles for [3+2] annulation with dipolarophiles for making functionalized tetrahydrofuran, pyrrolidine, and associated compounds. This review article covers recent development on epoxide- and aziridine-based [3+2] annulation reactions. The reactions are classified based on the ring opening conditions, including acid/base catalysis, organocatalysis, and transitional-metal catalysis.