Among all functional groups, alkynes occupy a privileged position in synthetic and medicinal chemistry, chemical biology, and materials science. Thioalkynes, in particular, are highly useful, as they combine the enhanced reactivity of the triple bond with a sulfur atom frequently encountered in bioactive compounds and materials. Nevertheless, general methods to access these compounds are lacking. In this article, we describe the mechanism and full scope of the alkynylation of thiols using ethynyl benziodoxolone (EBX) hypervalent iodine reagents. Computations led to the discovery of a new, three-atom concerted transition state with a very low energy barrier, which rationalizes the high reaction rate. On the basis of this result, the scope of the reaction was extended to the synthesis of aryl- and alkyl-substituted alkynes containing a broad range of functional groups. New sulfur nucleophiles such as thioglycosides, thioacids, and sodium hydrogen sulfide were also alkynylated successfully to lead to the most general and practical method yet reported for the synthesis of thioalkynes.