Unimolecular polymeric nanocontainers possess exclusive single molecular architecture with covalently bonded core-shell structure, which can maintain outstanding stability upon surrounding environmental changes and are suitable for various applications, including small molecules encapsulation for drug delivery, bio-imaging, reaction catalysis, and the generation of inorganic nanoparticles as templates. In this thesis, the one-pot chain-growth copolymerization of AB2 and AB monomers via the copper-catalyzed azide-alkyne cycloaddition (CuAAC) reactions is reported for the first time to tune the compositions and structures of (hyper)branched polymers for their application as unimolecular nanocontainers. The structural investigation provides more opportunity to synthesize functionalized hyperbranched polytriazoles (HBPs) via the post-modification at the periphery and in the interior of polymers. The chain-growth mechanism and living polymerization characteristic facilitate the production of branched polymers with low dispersity, varied sizes, tunable degrees of branching, and functionalities. The application of these affordable HBPs as unimolecular nanocontainers for bioimaging, drug delivery, and template for inorganic nanoparticles are investigated by encapsulating various functional payloads.