Complex networks contain various interactions among similar or different entities. These kinds of networks are called multi-relational networks, in which each layer corresponds to a special type of interaction. Multi-relational networks are a particular type of multilayer networks in which nodes are similar entities; however, edges or communications demonstrate different types of interactions among similar entities. In this survey, we study community detection methods for multi-relational networks. The considered models are divided into two main groups, namely, direct methods and indirect methods. We put indirect methods in two classes: flattening and ensembling, and the direct methods are further divided into four groups which are: probabilistic methods, algebraic methods, modular-based methods, and graph feature-based methods. For each approach and each method, we explain their pros and cons. Additionally, all the used datasets in the multilayer community detection studies are categorized into synthetic and real data. We elaborate on the most important datasets. Afterward, the utilized evaluation metrics by the papers are described. Finally, the current models' challenges and shortcomings are discussed. Finally, some suggestions for future research are developed. Putting all this together, this study, to the best of our knowledge, is the most comprehensive survey dedicated to multi-relational networks community detection.