This introduction presents an overview of the key concepts discussed in the subsequent chapters of this book. The book examines the different historical and geographical contexts in which extraterritorial regimes have developed, the myriad political and economic pressures in response to which such regimes have grown, the highly uneven distributions of extraterritorial privilege that have resulted from these processes. It demonstrates that assertions of legal authority ‘beyond’ territorial frontiers have always played a central role in the constitution and consolidation of sovereignty. The book explains extra-territorial jurisdiction in the legal strategies and ‘state spaces’ of US empire, both before and after the Second World War. It also explores the question of the extraterritorial application of the European Convention of Human Rights, one of the most controversial issues faced by the Strasbourg court. The book is concerned with the limitations of thinking about legal obligations through the prism of extraterritoriality.