The principle of territoriality poses significant challenges to the economic world in patent law. While patents continue to be designed as territorially limited rights, many inventions today focus on computer-based processes and systems that can be used across national borders. This work addresses the question of to what extent the cross-border use of process and system claims, considering the principle of territoriality, triggers liability for domestic patent infringement. The various forms of cross-border usage cases are examined and analyzed in a practical manner using a wide range of examples from the application and granting practice.