This chapter explores the relationship between data science, data crimes and the law. It illustrates how Big Data is responsible for Big Data crimes, but that data science and law could mutually help each other by identifying the ethical and legal devices necessary to enable Big Data analytic techniques to identify the key stages at which data crimes take place and also prevent them. This chapter will therefore explore the use of data science (Big Data) analytics for the fight against (cyber) crime and identify the implications for the law, and possible solutions. In particular, it discusses the literature on Big Data and Crime that considers the development of predictive models of crime that can be used to assist criminal justice professionals, such as police management, to allocate resources more efficiently. The authors contribute to this debate in three ways. The first contribution is theoretical and stems from a dialogue with data ethicists, as the authors propose that it is crucial to account for the endogenous and exogenous limitations of data science. Secondly, they demonstrate how Big Data itself has created new criminal markets for Big Data which encourage data crime. The development of which creates new challenges for law enforcement agencies on an unprecedented scale. The third contribution is that the much-hyped and much critiqued Big Data analytic techniques could actually be applied, in certain circumstances and subject to appropriate rules of engagement which take into account the nature of the data, to an analysis of data crime in order to help investigators understand it more thoroughly and possibly even detect the point of crimes to assist in the tracking of offenders.