With a decision based upon the consideration that all the significant conduct occurred outside the territory of the United States, in Kiobel the U.S. Supreme Court unanimously ruled that the presumption against extraterritoriality applies to claims under the Alien Tort Statute, and that nothing in the statute refutes that presumption. However, in its decision the Supreme Court did not directly address the issue whether a cor-poration can be a proper defendant in a lawsuit under the ATS. In this article, the Author begins by providing a substantial «pre-Kiobel» analysis of the business-human rights relationship. Furthermore, in addressing – with reference to the Kiobel case – the issues of corporate liability and extraterritorial jurisdiction over abuses committed abroad, the Author provides a detailed description of the governments’ positions on universal civil jurisdiction, also providing a critical evaluation of the arguments put forth by the EU Member States on the extraterritorial application of ATS. As the Author illustrates, this decision is far more complex and problematic than it may appear: it in fact leaves a number of questions open on what exactly remains of the ATS, as well as various uncertainties due to the substantive differences between the majority opinion and the different concurring opinions, difficult to be reconciled and harmonized, especially from an European standpoint.