In this paper we are presenting an overview of the existing works that have been published in the quantum optimization of neural networks and fuzzy systems, considering both theoretical contributions and applications. The analysis was done considering all kinds of publications: journal papers, chapters in books and conference papers. The database was obtained from Scopus system of Elsevier, which contains most of the indexed publications in the world in all areas. Recently, type-2 and type-3 fuzzy systems have been used to aggregate neural networks in forming ensemble models, but their optimization is challenging, so we expect that quantum optimization could be helpful in this area. Based on the obtained data, relevant conclusions were obtained about the development of the quantum optimization of neural networks and fuzzy systems, as well as future trends for this evolving field.