Neutrosophic set is a branch of neutrosophy concerned with nature, the genesis, and breadth of impartialities, and also their interaction with various mental spectra. Neutrosophic sets constitute relatively new expansions of intuitionistic fuzzy. In a short period of time, numerous researchers have accepted neutrosophic reasoning. Many researchers have linked neutrosophic science and metaheuristics in various ways over the last ten years. Metaheuristic research has attracted a great attention throughout the literature, which covers methodologies, apps, comparative analysis; due to its higher intensities and fruitful implementations. Metaheuristic algorithms are used to introduce the best or the optimum solutions to a lot of optimization problems due to the behavior of these algorithms inspired by Nature and its ability to adapt to problems, as well as the possibility of integrating more than one algorithm to reach the best solutions. Based on the previous reason, many researchers used these algorithms with neutrosophic science to present many platforms in the recent years, which was the motivation to introduce this survey paper. This paper is introduced to cover the publications from 2010 to 2021 in order to draw a comprehensive picture of metaheuristic research integrated with neutrosophic theory.