This chapter examines the issue of jurisdictional problems in competition law, the ‘internationalisation’ of competition law, and the efforts to deal with competition issues at a global level to match the global operations of undertakings on world markets. It looks first at the question of extraterritoriality in public international law, particularly the concept of objective territoriality. It considers the distinction between prescriptive jurisdiction and enforcement jurisdiction and how these might apply to competition law. It then looks at the development of the effects doctrine in US law and the concept of comity, and at the position of foreign plaintiffs in US courts. It considers how the EU takes jurisdiction by the application of the single economic entity doctrine, the implementation doctrine, and the qualified effects doctrine. The chapter concludes by examining international cooperation in competition law and how competition law must be sensitive to the huge global economic inequalities of the twenty-first century. It looks at the bilateral agreements into which the EU has entered, and the multilateral cooperation to which the EU is party, including cooperation within UNCTAD, the OECD, the WTO, and the International Competition Network (ICN).