In 2015, the United Nations agreed on 17 Sustainable Development Goals as the central normative framework for sustainable development worldwide. The effectiveness of governing by such broad global goals, however, remains uncertain, and we lack comprehensive meta-studies that assess the political impact of the goals across countries and globally. We present here condensed evidence from an analysis of over 3,000 scientific studies on the Sustainable Development Goals published between 2016 and April 2021. Our findings suggests that the goals have had some political impact on institutions and policies, from local to global governance. This impact has been largely discursive, affecting the way actors understand and communicate about sustainable development. More profound normative and institutional impact, from legislative action to changing resource allocation, remains rare. We conclude that the scientific evidence suggests only limited transformative political impact of the Sustainable Development Goals thus far.