We begin with a review of plastic card fraud: The nature and magnitude of the problem. This is followed by a description of the the data and the operational context in which data analysis procedures operate. Such procedures have to address specific problems including the rarity of fraudulent behaviour, the volume and velocity of the data, and the need to handle temporal variation. Supervised and unsupervised learning approaches are compared and contrasted. We conclude with a recommendation that the most flexible fraud detection systems will capitalise on carefully engineered combinations of supervised and unsupervised methods.