The rapid development of efficient organic click coupling reactions has significantly facilitated the construction of synthetic polymers with sophisticated branched nanostructures. This Feature Article summarizes the recent progress in the application of efficient copper-catalyzed and copper-free azide–alkyne cycloaddition (CuAAC and CuFAAC) reactions in the syntheses of dendrimers, hyperbranched polymers, star polymers, graft polymers, molecular brushes, and cyclic graft polymers. Literature reports on the interesting properties and functions of these polytriazole-based nanostructured polymers are also discussed to illustrate their potential applications as self-healing polymers, adhesives, polymer catalysts, opto-electronic polymer materials and polymer carriers for drug and imaging molecules.