This thesis examines the Council of Europe's Cybercrime Convention and suggests there is a structural imbalance: while improving the procedures for investigating cybercrimes, it has failed to address the prosecutorial complexities and disputes resulting from multijurisdictional cybercrimes, by following the usual trend of 'suppression' conventions. This trend is to expand the procedural mechanisms through which States can acquire evidence in relation to the 'suppressed' offences, while suggesting that State Parties adopt broad rules in relation to criminal jurisdiction. These procedural powers have provided powerful tools for policing cybercrime, and the Convention has been innovative by developing mechanisms for facilitating networking interactions between law enforcement, and on most interpretations, even providing for directly contacting foreign service providers for data. The traditional limitations of enforcement jurisdiction are gradually being transformed, but the resulting difficulties for jurisdictional concurrency are not appreciated. Given the malleability of the concept of 'territoriality', and the flexibility afforded in international law in its interpretation, seizures of jurisdiction over many cybercrimes have sometimes been on the most tenuous of grounds. This results in a problem of concurrent jurisdiction on a scale previously unseen in the context of other transnational offences. It is often assumed that once substantive criminal harmonisation occurs, jurisdictional conflict between States dissipates, but I highlight three areas where concurrency is beginning to generate difficulties: investigatory and prosecutorial negotiations, cybercrime extraditions, and the law relating to ne bis in idem. I argue that these problems are only going to be exacerbated given the inroads that are being made in investigative powers and enforcement jurisdiction, coupled with the global reach of cybercrime which brings more and more States into play. I provide both the theoretical and practical case for more refined approaches towards the concept of territoriality, and consider some of the potential mechanisms for dealing with these uneasy bedfellows in the Cybercrime Convention.