This chapter focuses on cybercriminal activities that cannot easily be regulated by states via existing means, either because new criminal elements are involved or because the scale and the transnational dimension of a particular activity necessitate international cooperation. While many crimes committed by means of a computer are not essentially new crimes and can be subsumed under extant definitions and be dealt with by domestic legal systems, some criminal activities require specific legal responses at the international level. The chapter gives an overview of these crimes, examines initiatives that have been undertaken to fight them, and discusses particular challenges, notably with respect to jurisdiction. It concludes that the various multilateral initiatives, above all the Council of Europe Convention on Cybercrime, are valuable, since they lay the groundwork for greater cooperation between states. However, more comprehensive approaches that integrate a deeper understanding of the functioning of information technology may be required. Global cooperation, beyond state or regional boundaries, and across the state/non-state divide, is needed to deal with many forms of cybercrime.