For the last six years, the International Federation for Human Rights and REDRESS have been collaborating to facilitate a common approach between the Member States of the EU on the implementation of extraterritorial jurisdiction. This report summarises the findings of a recent conference, in which our organisations brought together different national and international actors, including lawyers, human rights organisations, investigators, prosecutors and EU officials. Discussions focused on the central challenges relating to the exercise by Member States of extraterritorial jurisdiction, mutual cooperation, and the challenges associated with the investigation and prosecution of such crimes.