Click chemistry has drawn considerable attention in less than a decade due to its unique advantages, such as simple reaction conditions, high reaction efficiency, high yield, easy post-treatment and high selectivity for the obtained products. Recently, as a new and efficient click reaction, thiol-ene/yne click chemistry has raised much interest and will probably be the main direction for development in click chemistry. On the other hand, synthesis of high-performance functional polymer materials is one of the hot topics of novel material research. In this review, we introduce the characteristics, advantages and reaction mechanism of thiol-ene/yne click chemistry. Research progresses of thiol-ene/yne click chemistry in functional polymer synthesis are highlighted, with focus on the synthetic route of linear, hyperbranched, cross-linked and other types of functional polymers via this method. The monomer features, product features and potential applications of different types of functional polymer materials synthesized by thiol-ene/yne click reaction are also discussed in detail. Furthermore, the problems in thiol-ene/yne click chemistry that still should be resolved are pointed out, and future applications are prospected.