This interdisciplinary book explores the concept of convergence of the EU with the global legal order. It captures the actions, law-making and practice of the EU as a cutting-edge actor in the world promoting convergence 'against the grain'. In a dynamic 'twist' the book uses methodology to reflect upon some of the most dramatically changing dimensions of current global affairs. Questions explored include: who and what are the subjects and objects of convergence as to the EU and the world? How do 'court-centric' and less 'court-centric' approaches differ? Can we use political science and international relations as 'service tools'? Four key themes are probed: - framing EU convergence; - global trade against convergence; - the EU as the exceptional internationalist; and - positioning convergence through methodology.