The parallel development of reversible deactivation radical polymerization and click reaction concepts significantly enriches the toolbox of synthetic polymer chemistry. The synergistic effect of combining these approaches manifests itself in a growth of interest to the design of well-defined functional polymers and their controlled conjugation with biomolecules, drugs, and inorganic surfaces. In this review, we discuss the results obtained with reversible addition–fragmentation chain transfer (RAFT) polymerization and different types of click reactions on low- and high-molar-mass reactants. Our classification of literature sources is based on the typical structure of macromolecules produced by the RAFT technique. The review addresses click reactions, immediate or preceded by a modification of another type, on the leaving and stabilizing groups inherited by a growing macromolecule from the chain transfer agent, as well as on the side groups coming from monomers entering the polymerization process. Architecture and self-assembling properties of the resulting polymers are briefly discussed with regard to their potential functional applications, which include drug delivery, protein recognition, anti-fouling and anti-corrosion coatings, the compatibilization of polymer blends, the modification of fillers to increase their dispersibility in polymer matrices, etc.