The concept of 1,3‐dipolar cycloadditions was presented by Rolf Huisgen 60 years ago. Previously unknown reactive intermediates, for example azomethine ylides, were introduced to organic chemistry and the (3+2) cycloadditions of 1,3‐dipoles to multiple‐bond systems (Huisgen reaction) developed into one of the most versatile synthetic methods in heterocyclic chemistry. In this Review, we present the history of this research area, highlight important older reports, and describe the evolution and further development of the concept. The most important mechanistic and synthetic results are discussed. Quantum‐mechanical calculations support the concerted mechanism always favored by R. Huisgen; however, in extreme cases intermediates may be involved. The impact of 1,3‐dipolar cycloadditions on the click chemistry concept of K. B. Sharpless will also be discussed.