To explore the emerging and contested issue of business and human rights in the area of climate change, this article provides a critical discussion from the viewpoint of moral philosophy. A novel typology of businesses’ human rights duties (‘duty’ is considered synonymous with ‘responsibility’ here) is proposed. It claims that duties are both forward- and backward-looking. Cases of human rights litigation seeking remedy for climate-related harms are backward-looking, and duties should be determined on the basis of proportion of historical emissions, culpable knowledge and counter-acts to abate climate harms. Businesses’ forward-looking duties, however, depend on their power, privilege, interest and collective abilities. The typology is then assessed against the background of recent legal principles and instruments. It is concluded that moral duties of business reach beyond mere respect for human rights and national jurisdictions in the context of climate change.