This chapter examines several ways that the United States takes advantage of international law’s permissiveness and ambiguity to extend its criminal law, along with digitally based investigations, beyond US borders. The international law of jurisdiction opens the door to several strategies for defining domestic criminal law that enable its application to criminal conduct outside US territory, even for conduct with only marginal connections on US interests. The chapter aims first to identify with some precision how the US can employ – or exploit – international law’s territorial premises and ambiguities to reach conduct committed in other states’ territories. All states can pursue this goal through choices in drafting statutory offence elements. But the United States has additional advantages because it can also expand its jurisdictional ambit by leveraging the transnational nature of digital infrastructure and its singularly large domestic economy. The chapter then assesses some effects and implications of these US policies for other states as well as for criminal actors. Conclusions are mixed. Determining whether extraterritorial investigations and law enforcement serves only one state’s parochial interests, as opposed to many states’ common interests or shared norms, depends greatly on contextual details, contested assessments of efficacy, and trade-offs among competing values. Sometimes US policies serve broadly shared interests; in other instances, they can be counterproductive or show insufficient regard for other states’ interests.