A recent request by the Italian Constitutional Court to the Court of Justice of the European Union for a preliminary ruling concerning its previous judgment Taricco calls into question the still very controversial relationship between the principle of supremacy of EU law and the protection of fundamental rights – as recognised by the national constitutional traditions – in the implementation of EU law by Member States. This paper summarises the most remarkable aspects of this new controversy, highlighting its importance for the future of the EU law and, in particular, for the prospect of a closer cooperation among Union and Member States in criminal law mat- ters.