It has been well argued that cross-border cooperation among supervisory authorities in data privacy law (‘cooperation’), be it in the European Union (EU) or elsewhere, is still in its infancy. There is a critical need to strengthen such cooperation to cope with challenges posed by recent technological developments and globalisation in order to offer practical, effective and efficient protection of (the right to) data privacy. The present report looks comparatively at six areas of cross-border cooperation of relevant authorities provided for in the laws of the EU, i.e. in migration and border control, private international law, consumer protection, competition law, criminal justice and fundamental rights. It does so because some of cooperation mechanisms therein, or elements thereof, have proven to be mature, efficient and successful enough and thus could offer valuable input how to increase efficiency of cooperation in EU data privacy law. The present report concludes with 14 lessons to be adapted to the reality and needs of cooperation within the EU and justifies the way in which these lessons could be useful to that end.