Fraud in health insurance claims continues to impose significant financial and operational burdens on healthcare systems, especially as the volume and complexity of claims increase. Conventional rule-based detection mechanisms, although widely used, have limited adaptability to evolving fraud patterns and high-dimensional data environments. This limitation has driven a shift toward data-driven analytical approaches capable of identifying suspicious patterns more effectively. This systematic review synthesizes peer-reviewed, open-access studies published between 2020 and 2025 that applied rule-based, supervised, unsupervised, or hybrid methods for fraud detection in health insurance claims. A comprehensive search across major databases yielded fourteen eligible studies representing diverse systems, datasets, and methodological designs. The findings indicate a clear transition from traditional rule-based systems to machine learning approaches, particularly in addressing challenges such as label scarcity, class imbalance, and complex fraud patterns. Most studies focused on integrated medical claims, where pharmaceutical fraud was embedded rather than analyzed independently, highlighting a gap in service-specific research. Significant heterogeneity was observed in fraud definitions, preprocessing techniques, labeling strategies, and evaluation metrics, limiting cross-study comparability and emphasizing the need for greater methodological transparency. Across the literature, data-driven approaches are consistently positioned as decision-support tools rather than definitive solutions, reinforcing their role in complementing expert judgment and regulatory oversight. Overall, effective implementation requires context-aware design, reliable labeling, and rigorous real-world validation. Future research should prioritize domain-specific analyses, particularly in pharmaceutical fraud, and improve transparency to support scalable and responsible deployment.