The idea of using historical data about crime and other social processes to improve resource allocation of police forces has been one of the hot topics in policing discourse over the last years. While system providers present their success stories, pointing to decreasing crime rates in areas where their tools were implemented by local police forces, the evidence is not convincing. Problems of predictive policing will be discussed from a technical and data perspective and from a theoretical and conceptual perspective to demonstrate the limits and un-intended side effects of this new approach to doing police work.