One central ethical question with the Anthropocene concerns access and allocation that are closely linked to distributive justice. Building on a normative conception of sustainable development (Ott/ Döring), the paper asks which norms ought to steer political action and ethically inform governance with the Anthropocene. Two aspects will be specially dealt with: Firstly, what do we owe other contemporary and future human beings in a sustainable world? In answering this question, the paper employs two ethical approaches: human rights (Gewirth, Düwell) and human capabilities (Sen, Nussbaum). It then deals with the question to whom we have moral and political obligations and how do these insights translate into political rules. While both might look like mere theoretical questions, they might have practical impact on governance. The paper aims to advance the normative discussion on sustainable development in the Anthropocene.