Since the discovery of organic azides by Peter Grieß more than 140 years ago, numerous syntheses of these energy-rich molecules have been developed. In more recent times in particular, completely new perspectives have been developed for their use in peptide chemistry, combinatorial chemistry, and heterocyclic synthesis. Organic azides have assumed an important position at the interface between chemistry, biology, medicine, and materials science. In this Review, the fundamental characteristics of azide chemistry and current developments are presented. The focus will be placed on cycloadditions (Huisgen reaction), aza ylide chemistry, and the synthesis of heterocycles. Further reactions such as the aza-Wittig reaction, the Sundberg rearrangement, the Staudinger ligation, the Boyer and Boyer–Aubé rearrangements, the Curtius rearrangement, the Schmidt rearrangement, and the Hemetsberger rearrangement bear witness to the versatility of modern azide chemistry.