Fraud is costing billions of dollars to the insurance industry each year. As a result, numerous scholars and professionals have investigated the use of both standard econometric and machine learning techniques to detect fraudulent insurance claims. This chapter provides an overview of the main models used to prevent and detect insurance fraud, as well as the main challenges faced by modelers as part of this process. On the one hand, particular attention is paid to the evaluation of the gains in terms of statistical predictive performance when using machine learning models over traditional econometric models. On the other hand, an evaluation of the financial efficiency when switching from standard methods to cost-sensitive approaches is carried out. We illustrate empirically these issues by the means of logistic regression, random forest, and eXtreme Gradient Boosting (XGBoost) algorithms and their cost-sensitive counterparts. Results show that machine learning techniques perform better statistically and can also be more effective than standard approaches in reducing fraud-related costs. However, it is important to note that they must be accompanied by expert knowledge and human analysis to ensure accurate and reliable fraud detection in the insurance industry.