For the last thirty years, human rights litigation was an almost exclusive domain of U.S. federal courts. With the judgment of the U.S. Supreme Court in the Kiobel case this tradition was ended. The question is whether European jurisdictions are willing and able to take up the ball in cases involving European enterprises. The U.N. Guiding Principles on Business and Human Rights require »human rights due diligence« from firms, and require states to provide for effective remedies. This raises complex issues of jurisdiction, choice of law, and extra-contractual liability. Jurisdiction does not place a major hurdle as, under the Brussels I Regulation, companies headquartered or incorporated within the EU may readily be sued in their home state. Regarding choice of law however, the Rome II Regulation follows the principle of lex loci damni, designating the law of the place where the injury was sustained, and this place is usually located abroad. The resultant obstacle to human rights litigation cannot be overridden with the help of considerations of public policy. As far as substantive liability regimes are concerned, they rest on a fundamental principle, rarely brought to the fore, that individuals and firms are responsible for their own actions and omissions only, not for the behaviour of third parties. With regard to corporate groups involving parents and subsidiaries, human rights litigation challenges the principle of »entity liability« and draws on notions of »enterprise liability« that treat a group of companies like a single firm with each unit being liable for the behaviour of any other unit. Holding European companies liable for the actions of their suppliers and business partners overseas calls a well-established principle of vicarious liability into question, namely that it does not extend to independent contractors. It seems impossible to relax these principles with regard to cases of human rights violations only, as human rights are indistinguishable from the rights protected under the law of delict or tort.