Like a hydra, fraudsters adapt and circumvent increasingly sophisticated barriers erected by public or private institutions. Among these institutions, banks must quickly take measures to avoid losses while guaranteeing the satisfaction of law-abiding customers. Facing an expanding flow of operations, effective banking relies on data analytics to support established risk control processes, but also on a better understanding of the underlying fraud mechanism. In addition, fraud being a criminal offence, the evidential aspect of the process must also be considered. These legal, operational, and strategic constraints lead to compromises on the means to be implemented for fraud management. This paper first focuses on the translation of practical questions raised in the banking industry at each step of the fraud management process into performance evaluation required to design a fraud detection model. Secondly, it considers a range of machine learning approaches that address these specificities: the imbalance between fraudulent and nonfraudulent operations, the lack of fully trusted labels, the concept-drift phenomenon, and the unavoidable trade-off between accuracy and interpretability of detection. This state-of-the-art review sheds some light on a technology race between black box machine learning models improved by post-hoc interpretation and intrinsic interpretable models boosted to gain accuracy. Finally, it discusses how concrete and promising hybrid approaches can provide pragmatic, short-term answers to banks and policy makers without swallowing up stakeholders with economical and ethical stakes in this technological race.