How do the goals, targets and indicators of the Sustainable Development Goals (SDGs) serve as governance instruments in efforts to achieve the SDGs by 2030? This perspective addresses this question in three sections. First, it develops an account of how we should understand governance for the SDGs that highlights the role of targets and indicators, but also institutions and norms, in this model of ‘soft’ governance. Second, it then offers a brief assessment of how the SDGs have worked as governance innovation since 2015, highlighting changes in the infrastructure of the SDGs and some national contexts, but also limitations. This section also considers the place of national ownership as a principle, integral to the SDGs, which constrains the transformative potential of the goals and targets. A final section considers how elements and mechanisms of SDG governance might be developed further. It points toward the importance of scaling up pockets of innovation and goal achievement across jurisdictions and levels of governance, while raising questions about expectations for SDG achievement beyond 2030.