This paper offers insights and perspectives on the jurisdiction of law enforcement authorities (LEAs) under international law and reviews current approaches to the territoriality principle and trans-border access to data for LEAs to conduct criminal investigations, controversial topics that are currently in the center of discussions, both at the international and national level. The views and perspectives offered in this paper seek to contribute to the international debate on cross-border access to data by LEAs and how the principles on internet jurisdiction should evolve in order to turn the administration of the criminal justice system more efficient, dynamic and compliant with the needs to obtain and secure evidence while respecting data protection safeguards.