This highlight presents an overview of our recent achievements on developing a chain-growth copper-catalyzed azide–alkyne cycloaddition (CuAAC) polymerization of multifunctional ABm (m ≥ 2) monomers to produce structurally defined hyperbranched polymers in one pot. The chain-growth mechanism is attributed to the dedicate complexation between copper(I) catalyst and triazole groups that confine the copper catalyst in the polymers and selectively favor the polymer–monomer reaction rather than the monomer–monomer reactions. The living nature of this CuAAC polymerization was extensively explored to demonstrate the intriguing features of multibatch addition of various AB2 monomers to produce hyperbranched polymers with high molar mass, low dispersity, core-shell segmented structures, and tunable solubility. 1 Background 2 Development of Living Chain-Growth CuAAC Polymerization 3 Functionalization and Segmented Structure in Hyperbranched Polymers 4 Conclusion