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Fraud, corruption, and collusion are the most common types of crime in public procurement processes; they produce significant monetary losses, inefficiency, and misuse of the public treasury. However, empirical research in this area to detect these crimes is still insufficient. This article presents a systematic literature review focusing on the most contemporary data-driven techniques applied to crime detection in public procurement. The preferred reporting items for systematic reviews and meta-analyses (PRISMA) methodology was adopted to identify typical elements that lead to crimes in public contracting. We collected scientific papers and analyzed the selected research using the Scopus repository. We evaluated and summarized findings related to crime detection techniques based mainly on machine learning and network science, as well as studies using fraud risk indices. Some methodologies presented promising results in identifying crimes, especially those using labeled data and machine learning techniques. However, due to the frequent unavailability of pre-labeled data on past cases, analysis through network science tools has become more evident and relevant in exploratory research.