The fascinating chemical properties of N-heterocyclic carbene (NHC) complexes showed them to be a suitable class of complexes to be investigated for their applications as drugs in the treatment of the infectious disease or cancer. In particular, the great structural versatility provided a library of compounds with a low cytotoxic profile, suitable candidates as new anticancer agents. Most of these complexes have shown higher cytotoxicity than cisplatin. In the present review, the medicinal applications of copper(I)- and silver(I)-NHC complexes are summarized. Specifically, azolium precursors and related Cu(I)- and Ag(I)-NHC complexes of functionalized and non-functionalized imidazole-, and benzimidazole-based NHC complexes studied as an alternative to cisplatin as chemotherapeutic agents are reviewed. An outline of the most significant chemical features is presented: copper(I)- and silver(I)-NHC complexes tested as anticancer drugs have been reported and a description of structure-activity relationships was made as far as possible.