During the last decades, great efforts have been devoted to design polymers for reducing the toxicity, increasing the absorption, and improving the release profile of drugs. Advantage has been also taken from the inherent multivalency of polymers and dendrimers for the incorporation of diverse functional molecules of interest in targeting and diagnosis. In addition, polymeric hydrogels with the ability to encapsulate drugs and cells have been developed for drug delivery and tissue engineering applications. In the long road to this successful story, pharmaceutical sciences have been accompanied by parallel advances in synthetic methodologies allowing the preparation of precise polymeric materials with enhanced properties. In this context, the introduction of the click concept by Sharpless and coworkers in 2001 focusing the attention on modularity and orthogonality has greatly benefited polymer synthesis, an area where reaction efficiency and product purity are significantly challenged. The purpose of this Expert Review is to discuss the impact of click chemistry in the preparation and functionalization of polymers, dendrimers, and hydrogels of interest in drug delivery.