The main objective of business and human rights dialogue is to expand somehow the (international) human rights obligations to multinational enterprises, transnational companies and other business entities. It is more than the corporate social responsibility as softly tries to create enforceable duties for companies beyond the self-regulation, and establish the grounds of their accountability for human rights violations. In constitutional legal terms it leads to the question of third party effect of human rights on the one hand and extraterritorial jurisdiction of the national courts on the other. As a related problem, the constitutional background of the application of international law by the courts can also be mentioned. The study gives an overview on the efforts of the United Nations and the European Union for responsible business, and analyses the related constitutional difficulties with regard to the landmark Kiobel decision of the US Supreme Court.