The application of EU law beyond its borders has occasionally been contested on the basis that it is claimed to infringe the sovereign rights of third countries. Extraterritoriality, in the strict sense, is traditionally seen as being inconsistent with principles of territorial sovereignty and non-interference in internal affairs: ‘territorial sovereignty belongs always to one [...] to the exclusion of all others’. However, there is a movement ‘towards bases of jurisdiction other than territoriality’, particularly in the field of criminal law, where the principles of active and passive nationality are usually accepted and the principle of universal jurisdiction is increasingly applied. Furthermore, some international subjects, including the EU, have justified the ‘territorial extension’ of their laws by invoking the ‘effects doctrine’: for instance, the fact that an undertaking participating in an anticompetitive agreement is situated in a third country does not prevent the application of EU competition rules if that agreement is effective in the EU territory. The contributions contained in this publication address several issues regarding the application of EU law beyond its borders.