I was invited to deliver this research seminar in my capacity as a visiting scholar: The assertion of extraterritorial jurisdiction by nation states is not inherently cosmopolitan. Rather, it is a double-edged sword. This is because extraterritorial jurisdiction is capable of being wielded for both cosmopolitan and non-cosmopolitan purposes: for empowerment, but also oppression; for rescue, but also retribution; for protection, but also unilateral political gain. In that context, this chapter introduces the law of extraterritorial jurisdiction, considers why states might wish to exercise it, and then identifies arguments both for (such as universalism, and the avoidance of impunity) and against (such as the undermining of meaningful multilateralism and the rights of an accused) exercises of extraterritorial jurisdiction. Ultimately, this chapter concludes that extraterritorial jurisdiction can only be considered capable of furthering cosmopolitan ideals if certain criteria are met.