Fraudulent insurance claims pose a significant financial burden on the insurance industry, necessitating robust anomaly detection systems. Anomaly detection in insurance claims is a crucial task to identify fraudulent or irregular claims, reducing financial losses and improving business efficiency. Recent advancements in Machine Learning and data analytics have led to the development of Hybrid algorithms that combine different techniques to detect anomalies. This review article provides a comprehensive overview of hybrid algorithms for fraud detection in insurance claims discussing their strengths and weaknesses, limitations and applications. We explored various hybrid approaches including ensemble methods, fusion models and hierarchical algorithms and examined their performance in detecting different types of anomalies. Our review highlighted the potential of hybrid algorithms in improving anomaly detection accuracy and reducing false positives and discussed the future research directions for further enhance their effectiveness in the insurance industry.