<p>Community detection in social networks, especially within networks featuring multiple relationships, stands out as a promising research avenue. Due to the complexities inherent in these systems, numerous criteria have been proposed to evaluate the composite community structure of multilayer networks. Despite this field’s evolution, no comprehensive studies in the literature summarize the existing advances in this direction. To fill this critical gap and offer a valuable contribution to the community, this paper aims to provide a detailed and comprehensive review of community detection metrics within multilayer networks. We propose a two-level classification of various optimization criteria: the first level is based on optimization type, which depends on the number of metrics used, and the second level is based on the search strategy employed. By presenting this taxonomy, we aim to guide future research and applications in this dynamic field. </p>