Chapter 4 provides an incisive introduction to criminal jurisdiction and the internet, setting the scene for the chapters on jurisdiction of the criminal courts (Chapter 5) and investigative jurisdiction (Chapter 6). It explains the concurrency of criminal jurisdiction in international law and analyses the problems arising. In particular, there are two main conflicts of jurisdiction: first, the multiple, overlapping claims of jurisdiction between several states and the risk of multiple prosecutions for the same crime (or no prosecutions, as no state has sufficient evidence or motivation; second, jurisdictional overreach where conduct is lawful in one country, but a criminal offence in another country who wishes to prosecute, potentially causing jurisdictional overreach and spill-over effects. The chapter begins by setting out the grounds of jurisdiction under international law. An examination of the cross-border implications of cybercrime follows, distinguishing three discrete aspects of the cross-border nature of cybercrime and analysing the nature of jurisdictional conflicts under the lens of territoriality and connecting factors. It analyses how a better coordination of jurisdictional claims might be achieved under comity and reasonableness principles, and coordination under EU law, such as the Eurojust Guidelines and the EU Framework Decision. Finally, it critically analyses the ambit of double jeopardy and the ne bis in idem principles and their limited application. Conflicts of criminal jurisdiction, and the potential of multiple prosecutions of defendants for the same offence, call for greater international cooperation between states and coordination rules between different legal orders. However, the development of coordination rules in respect of national criminal jurisdiction is in its infancy.