The Introduction to this book introduces the concept of the extraterritorial or global reach of EU law, encompassing the extraterritorial application of EU law, territorial extension and the so-called ‘Brussels Effect’ through unilateral, bilateral and multilateral legal instruments, and explores its significance for the EU’s external relations and its identity as an international actor. It introduces the contributions of the subsequent chapters on specific fields of law and policy, including the environment, the internet and data protection, banking and financial markets, competition policy and migration. Finally, it offers some conclusions to the research findings of the book, exploring the ways in which law shapes the EU’s external identity and its relations with other legal regimes, both enabling and constraining the EU’s external action, and making the case for a normative perspective.