Recent times have witnessed a significant decline in the number of persons seeking asylum on the territory of European Union (EU) countries. When these trends are observed in the light of Member States’ continuous tightening of their border controls, it seems evident that access to the territory and to the asylum procedure is being seriously obstructed in the EU. Border management activities are no longer confined to the physical frontiers of the Member States or to the external borders of the EU; instead, their scope has been extended well beyond these, towards the high seas and into the territory of third countries. From the European Council on Refugees and Exiles (ECRE), a pan-European network of refugee-assisting NGOs working in 30 countries, we emphasise that Member States’ obligations under international and European refugee and human rights law do not stop at the physical boundaries of the EU. This includes interception operations taking place in the high seas or in the territorial waters of third countries. The EU and the Member States should recognise that the power to prevent access to the territory carries with it the responsibility to protect those in need.