The endorsement of the United Nations Guiding Principles on Business and Human Rights (UNGPs) triggered a remarkable process accelerating the recognition of human rights responsibilities for corporations in law and governance. Perhaps even more important is the emergence of an authoritative narrative on business and human rights (BHR), which arguably has the potential to overcome the often-fragmented approach to global issues. This article discusses the degree to which the BHR narrative has been able to penetrate competing powerful narratives that shape societal and regulatory responses. To what extent is the need to address the responsibility and accountability of corporations for human rights violations acknowledged? This is an especially pertinent question where it concerns imminent major global challenges such as climate change, which poses one of the greatest threats to human rights. Two major milestones of the last decade in the area of (environmental) sustainability are analysed: the Paris Climate Agreement and the Sustainable Development Goals. What role does the BHR narrative play in this context?