In smart grids, homes are equipped with smart meters (SMs) to monitor electricity consumption and report fine-grained readings to electric utility companies for billing and energy management. However, malicious consumers tamper with their SMs to report low readings to reduce their bills. This problem, known as electricity fraud, causes tremendous financial losses to electric utility companies worldwide and threatens the power grid’s stability. To detect electricity fraud, several methods have been proposed in the literature. Among the existing methods, the data-driven methods achieve state-of-art performance. Therefore, in this paper, we study the main existing data-driven electricity fraud detection methods, with emphasis on their pros and cons. We study supervised methods, including wide and deep neural networks and multi-data-source deep learning models, and unsupervised methods, including clustering. Then, we investigate how to preserve the consumers’ privacy, using encryption and federated learning, while enabling electricity fraud detection because it has been shown that fine-grained readings can reveal sensitive information about the consumers’ activities. After that, we investigate how to design robust electricity fraud detectors against adversarial attacks using ensemble learning and model distillation because they enable malicious consumers to evade detection while stealing electricity. Finally, we provide a comprehensive comparison of the existing works, followed by our recommendations for future research directions to enhance electricity fraud detection.