Although the perfectly branched dendrimers with degree of branching (DB) and molecular weight distribution (Mw/Mn) of 1 are very promising structures, the tedious multistep synthesis and inefficient chromatographic purification have led to attempts to replicate their structural properties via synthesis of hyperbranched polymers with high DB and low polydispersity in one-pot processes. The chain-growth CuI-catalyzed azide-alkyne cycloaddition polymerization (CuAACP) to produce structurally defined hyperbranched polymers in one pot, is discussed in the thesis. The chain-growth mechanism is attributed to the dedicate complexation between CuI catalyst and triazole groups that confine the Cu catalyst in the polymers and selectively favor the polymer-monomer reaction rather than the monomer-monomer reactions. The living nature of this CuAACP is extensively explored to demonstrate the intriguing features of multiple-batch addition of various AB2 monomers to produce hyperbranched polymers with high molar mass, low dispersity, core-shell segmented structures and orthogonal functionalities.