New methods to synthesize and functionalize polymers are of constant interest to the polymer scientist. The 1,3-dipolar cycloaddition between an azide and terminal alkyne has received much attention since the reports that copper(i) provides high yields and regioselective synthesis of 1,4-substituted 1,2,3-triazoles. This coupling chemistry has been rapidly adopted by polymer scientists in the synthesis and post-polymerization modification of polymers. This Review will provide the historical context of the recent development of the copper-mediated azide–alkyne cycloaddition and its use in polymer science, particularly in dendrimer synthesis/functionalization, surface immobilization/modification, orthogonally functionalizing polymers, and its integration with ATRP (atom transfer radical polymerization).