The EU is bound by human rights obligations toward individuals outside the territory of its Member States who are affected by its trade and investment policies. Internal rules of the EU, namely the Founding Treaties and the Charter of Fundamental Rights, and various external norms, that is international law sources, impose human rights obligations on the EU. Those human rights obligations are increasingly interpreted by treaty monitoring bodies as requiring extraterritorial due diligence duties from States parties, in the sense that the creation of substantial and foreseeable effects outside the State’s territory establishes the jurisdiction of the State party. This jurisdiction leads to positive obligations, namely the duty to exert due diligence on trade and investment policies. The EU is expected to assess the risks of human rights violations by its trade and investment partners in and outside its Member States and take all reasonable efforts to avoid foreseeable human rights violations. Although those human rights are likely to continue to be unenforceable before the Court of Justice, the consistent reference to due diligence obligations by treaty monitoring bodies, the European Ombudsman and the European Data Protection Supervisor should encourage EU institutions to comply with their due diligence obligations.