Until the year 2000, gold compounds were considered catalytically inert. Subsequently, it was found that they are able to promote the nucleophilic attack on unsaturated substrates by forming an Au–π-system. The main limitation in the use of these catalytic systems is the ease with which they decompose, which is avoided by stabilization with an ancillary ligand. N-heterocyclic carbenes (NHCs), having interesting σ-donor capacities, are able to stabilize the gold complexes (Au (I/III) NHC), favoring the exploration of their catalytic activity. This review reports the state of the art (years 2007–2022) in the nucleophilic addition of amines (hydroamination) and water (hydration) to the terminal and internal alkynes catalyzed by N-heterocyclic carbene gold (I/III) complexes. These reactions are particularly interesting both because they are environmentally sustainable and because they lead to the production of important intermediates in the chemical and pharmaceutical industry. In fact, they have an atom economy of 100%, and lead to the formation of imines and enamines, as well as the formation of ketones and enols, all important scaffolds in the synthesis of bioactive molecules, drugs, heterocycles, polymers, and bulk and fine chemicals.