This paper explores the United Nations’ Sustainable Development Goals (SDGs) in the context of EU action to promote the contribution of business to sustainability. Using the planetary boundaries and the ‘safe and just space’ framework , this paper interrogates what a research-based multidimensional concept of sustainability means for the implementation of the SDGs. We start out with what it means to be operating within the limits of our planet. Moving on to the concept of securing social foundations for humanity now and for the future within planetary boundaries, we discuss what this entails in terms of social justice, touching on a number of issues that do not seem to have been sufficiently integrated in the SDGs and EU’s follow-up. We then explore risks of continued unsustainability, with a particular focus on business. We further discuss EU initiatives to promote sustainable business. We summarise the gaps the paper has identified, in research, both conceptually and applied, in policy, and in strategies for achieving sustainability, concluding with reflections on the unprecedented collaboration across and beyond academia that would be required to implement the SDGs in a manner that ensures sustainability.