EU responses to maritime boundary disputes reveal certain paradoxes of governance. The increasing interest of EU States in controlling larger maritime areas and the public and private exploitation of marine and seabed resources are enhancing the territorialisation of the sea. The EU as a political project claims to transcend state-vested interests, promoting peaceful dispute resolution when it comes to maritime boundary disputes. This article highlights common drivers of maritime boundary disputes involving Member States and the role played by the EU in solving them (or not). Our purpose is to provide an investigative introduction that can aid further analyses, by showing that EU membership is not in itself sufficient to address historical antagonisms, geographical realities and national/economic interests when it comes to the maritime space. However, the EU does have a positive role to play as a facilitator of diplomatic negotiation, potentially holding both stick and carrot. The current Blue Growth agenda naturally calls for the settlement of disputes and the peaceful use of the oceans, but it can also play a role in feeding them via the incentivisation of actors involved in profit-generating activities at sea.