Since the 1968 Brussels Convention EU civil procedure law has grown largely both in numbers of legal instruments and in intensity. However, the existing EU Regulations have an EU-internal focus. Relations with third countries are dealt with in a disparate manner. This is suboptimal for cooperation with non-EU countries. Therefore, the EU has concluded the Lugano Convention with some European countries, but this is not a globally suitable approach. Based on comparative analyses and country-specific reports (EU member countries as well as non-EU countries), the book develops a structured approach for future action, be it by modification of existing EU regulations, passing new regulations, negotiating new multilateral or bilateral treaties (e.g. in the framework of the Hague Conference on Private International Law), developing soft law or passing national legislation, preferably on a uniform or coordinated basis together with third countries. The book deals also with Brexit issues.