This review covers recent achievements in metal‐catalyzed Z−H and Z−Z (Z=S, Se) bond addition to the triple bonds of alkynes—a convenient and atom‐efficient way to carbon‐element bond formation. Various catalytic systems (both homogeneous and heterogeneous) developed to date to obtain mono‐ and bis‐chalcogen‐substituted alkenes or dienes, as well as carbonyl compounds or heterocycles, starting from simple and available alkynes and chalcogenols or dichalcogenides are described. The right choice of metal and ligands allows us to perform these transformations with high selectivities under mild reaction conditions, thus tolerating unprotected functional groups in substrates and broadening ways of further modification of the products. The main aim of the review is to show the potential of the catalytic methods developed in synthetic organic chemistry. Thus, emphasis is made on the scope of reactions, types of products that can be selectively formed, convenience, and scalability of the catalytic procedures. A brief mechanistic description is also given to introduce new readers to the topic.