Click chemistry has revolutionized polymer science by providing efficient, orthogonal, and highly selective strategies for the synthesis and functionalization of macromolecules. Among these, copper(I)-catalyzed azide-alkyne cycloaddition (CuAAC) and strain-promoted azide-alkyne cycloaddition (SPAAC) stand out as powerful tools for constructing complex polymer architectures under mild conditions. These transformations have enabled unprecedented control over polymer composition, topology, and functionality, supporting the development of advanced materials for biomedical, electronic, and energy-related applications. This chapter offers a comprehensive overview of azide-alkyne cycloadditions in polymer science, emphasizing their applications in step-growth polymerization, block copolymer synthesis, and grafting techniques. Furthermore, we explore how CuAAC and SPAAC have facilitated the creation of smart materials, including polymeric prodrugs, gene delivery vectors, hydrogels, and proton- and electron-conductive membranes.