This is the first systematic review on the synthesis and reactions of heterocyclic azides with acetylene and acetonitrile derivatives, alkenes, enamines and dicarbonyl compounds. Examples are given for the application of these reactions to the synthesis of mono-, bi- and tricyclic compounds and ensembles of various heterocycles, e.g., azines and azoles (including 1,2,3-triazole derivatives and nonaromatic 1,2,3-triazolines), amidines and diazo compounds. Methods for the synthesis of supramolecular structures, coordination compounds, ligands, bioconjugates and biologically active compounds based on reactions with heterocyclic azides are considered. The review describes the use of these transformations in biological chemistry to study processes in living systems, as well as in materials chemistry for the production of luminophores and sensors for metals. Original studies published mainly over the past 15 years are discussed. Bibliography -- 222 references.