The research on using thiol-ene click reaction to synthesize sulfur-containing polymers with topological structures and advanced functional properties is a hot topic. However, the application of the thiol-yne reaction in the functional polymer preparation is limited and the thiol-yne click polymerization is to be further developed. In this review, we summarized recent research efforts on using thiol-yne click polymerization to synthesize polymers with topological structures. The sulfur-containing polymers were facilely prepared by photo- and thermo-initiated, amine-mediated, and transition-metal-catalyzed thiol-yne click polymerizations. These polymers are promising to be used as drug-delivery vehicles, high refractive index optical materials, photovoltaic materials, and biomaterials etc.