Metal-catalyzed hydrofunctionalization reactions of alkynes, i.e., the addition of Y–H units (Y = heteroatom or carbon) across the carbon–carbon triple bond, have attracted enormous attention for decades since they allow the straightforward and atom-economic access to a wide variety of functionalized olefins and, in its intramolecular version, to relevant heterocyclic and carbocyclic compounds. Despite conjugated 1,3-diynes being considered key building blocks in synthetic organic chemistry, this particular class of alkynes has been much less employed in hydrofunctionalization reactions when compared to terminal or internal monoynes. The presence of two C≡C bonds in conjugated 1,3-diynes adds to the classical regio- and stereocontrol issues associated with the alkyne hydrofunctionalization processes’ other problems, such as the possibility to undergo 1,2-, 3,4-, or 1,4-monoadditions as well as double addition reactions, thus increasing the number of potential products that can be formed. In this review article, metal-catalyzed hydrofunctionalization reactions of these challenging substrates are comprehensively discussed.