Most of the global initiatives in the field of artificial intelligence are designed as globally minded soft regulation. In the field of AI, “soft” law or the Brussels Effect can complement but will not be able to replace “hard” law. Various states not only have different approaches towards AI but also different values, interests, and capabilities. Therefore, AI constitutes an area in which, at least for the time being, it is impossible to reach any meaningful and enforceable consensus on the international level. This paper analyses the experience that we have so far with the extraterritorial enforcement of the GDPR, which, similarly to the AI Act, bases its territorial scope on the moderate destination approach. It discusses similarities but also differences, such as the expected limited impact of the AI Act-related Brussels Effect. A proven record of enforcing the AI Act outside of the Member States’ borders would boost the EU’s credibility and increase its significance in any international forums that work on AI-related issues. Effective extraterritorial enforcement would also be crucial for the success of the EU’s model of regulating AI, Europe’s role in the globalised world and for limiting the power asymmetry between global AI players and the EU. If successful, it could, for example, help us in creating more ethical AI not only in the EU but globally. It could also contribute to the strengthening of the EU’s digital sovereignty. To achieve these results the EU needs a toolbox and procedures that would facilitate extraterritorial enforcement of the AI Act. On the other hand, a lack of sufficient enforcement would question the legitimacy of the EU in this area and, ultimately—the credibility of the digital regulatory model adopted by the Union. In this context, the paper concludes that there is an urgent need for a discussion about extraterritorial enforcement of the AI Act.