Why is Big Data absent in the recent basic data protection documents of the European Union (EU) and the Council of Europe (CoE)? Why not one single reference to Big Data practices - be it to regulate or to prohibit it - in the recent General Data Protection Regulation (EU) 2016/679, the Data Protection Law Enforcement Directive (EU) 2016/680 and the Modernised CoE Convention 108 for the Protection of Individuals with Regard to the Processing of Personal Data (Convention 108+)? Some actors in the policy field considered Big Data too dan- gerous and counted on existing data protection principles to tame the beast. Others simply ignored the phenomenon or were not aware of the potential benefits of Big Data for economy and governments (the rendez-vous was missed). Our discussion of no less than six recent initiatives, - standalone laws and soft law instruments - is an indication that Europe is embracing Big Data but is seemingly hesitant to confront Big Data within the classical paradigm (field) of data protection law. Concrete guidance for Big Data practices is now spread over multiple texts emanating outside the data protection field.