Introduction1,3 -Dipolar cycloaddition reactions provide direct access to a wide range of useful heterocyclic systems. Many such heterocycles are found in natural products, manmade drugs, agrochemicals, and materials. As " fusion " processes, dipolar cycloadditions are atom -economical, and the variety of readily accessible dipoles and dipolarophiles make these transformations particularly suitable for the synthesis of structurally and functionally diverse collections of compounds. This large family of reactions has been a subject of intensive research, notably by Rolf Huisgen and coworkers, whose work led to the formulation of the general concept of 1,3 -dipolar cycloadditions in 1958 [1] . Since then, dipolar cycloaddition chemistry has found extensive applications in organic synthesis and has been the subject of several reviews [2,3] .Organic azides represent a unique component of cycloaddition processes because R -N 3 is the only 1,3 -dipolar reagent that can be made, handled, and stored as a stable entity. Until recently, the cycloaddition reactions of azides with olefi ns received greater attention among organic chemists than the corresponding reactions with alkynes. Yet, the azide -alkyne combination is uniquely useful for three main reasons. First, the product 1,2,3 -triazole is a remarkably stable aromatic structure that can serve, among other roles, as a structural analogue of a peptide linkage. Second, the azide -alkyne reaction is remarkably slow for a process that is thermodynamically favorable by more than 50 kcal mol − 1 . Finally, azides and alkynes are relatively nonpolar, neither acidic nor basic, and are devoid of substantial hydrogen bonding ability, properties that make them quite " invisible " to and unreactive with most other chemical functionalities in nature and the laboratory. Azides and alkynes can, thereby, be installed on structures that one wishes to link together, and kept in place through many operations of synthesis and elaboration. They are ideal connectors for such a modular approach to synthesis, if effective methods to catalyze their cycloaddition are available. This chapter describes the catalytic role of copper complexes that has allowed this general scheme to be put in operation for a wide array of applications and settings.