Looking back at the past reveals the future – that is, in a nutshell, the big promise of Big Data. By applying high-performance computer technology and specifically adapted statistical methods to large amounts of data, scientists strive to extract patterns from past human behaviour which they deem likely to reappear in the future (so-called predictive analytics). With predictive policing state authorities try to harness Big Data to predict future crimes and other threats to public safety and security and to prevent them before they materialise. The first aim of this paper is to illustrate in what areas this emerging technology is being tested or already applied. Applications range from predicting burglaries and assaults likely to be committed in specific neighbourhoods or by specific individuals to forecasting acts of international terrorism under the new German PNR legislation (Fluggastdatengesetz). Next, the paper examines in detail whether and to what extent predictive policing is merely a faster and more efficient equivalent to traditional, i.e. human, investigative methods. The paper finds that there are indeed similarities and differences between human policing and automated pattern recognition that require and – at the same time – justify a cautious use of predictive policing: pattern-based predictions may be used to trigger further human investigation (Gefahrerforschungseingriffe), but cannot as such justify final determinations with adverse effects to individuals (Gefahrbeseitigungseingriffe). To what extent further investigation may be justified in the circumstances of individual cases then largely depends on how specific and how reliable the patterns are, and on whether it is possible to rule out unqualified reliance on discriminating criteria such as race, religion, sexual orientation etc. If specificity, reliability and non-discrimination can be provided, the case law of the German Constitutional Court concerning the right to informational self-determination, which in effect forbids dragnet-investigations (Rasterfahndung), does not preclude predictive policing. Then, authorities may use the tool, in principle, to identify potential threats to public safety and security. However, there are good reasons to oppose comprehensive surveillance even if it is (almost) perfect, i.e. specific, reliable and non-discriminatory. The concluding sections of the paper explain why that is so and develop criteria for the application of predictive policing that help to prevent a slippery slope towards comprehensive surveillance. Finally, these criteria are tested on the new German PNR legislation, with ambivalent results.