Click polymerization, a powerful synthetic technique to construct polymers with unique structures and advanced functions, is of crucial importance in the areas of polymer and material sciences. A variety of click polymerizations such as azide-alkyne, thiol-yne, amino-yne, and hydroxyl-yne reactions have been established, wherein the catalytic systems play an indispensable role in realizing these highly practical reactions based on triple-bond building blocks, as they directly influence the efficiencies of the click polymerizations and the performances of the resultant polymers. The vital employment of catalysts is reviewed and their developments from innovative discoveries to the eminent position are outlined. Moreover, the challenges and perspectives in this area are also briefly discussed.