International organizations face a highly complex task: to detect money-laundering operations, which, because of their illegality, tend to remain hidden from the authorities. One of the most valuable assets is the information centralized by these control bodies such as alerts generated by financial institutions based on transactional transactions, which, because of their large volume, requires an advanced strategy to identify unusual operations that, despite efforts, remain a challenge. For this reason, a systematic review of the literature on generating money-laundering alerts based on complex networks was developed. This review found that the analysis of complex networks is ideal given its ability to identify criminal patterns in a large volume of transactional data and also presents challenges for when the network is incomplete, and the origin or destination of resources is unknown. © 2021, Associacao Iberica de Sistemas e Tecnologias de Informacao. All rights reserved.