•Three governance challenges to implementing the SDGs are identified and discussed.•Collective action across sectors, levels and scales will be required.•Win–wins may not be possible so tradeoffs must focus on equity, justice and fairness.•Mechanisms are needed to ensure accountability for reaching targets and outcomes.•Challenges influence each other; implementation must take an integrated approach. Realising the aspirations of the “Sustainable Development Goals” (SDGs) to reduce inequality, limit ecological damage, and secure resilient livelihoods is a grand challenge for sustainability science, civil society and government. We identify three key governance challenges that are central for implementing the SDGs: (i) cultivating collective action by creating inclusive decision spaces for stakeholder interaction across multiple sectors and scales; (ii) making difficult trade-offs, focusing on equity, justice and fairness; and (iii) ensuring mechanisms exist to hold societal actors to account regarding decision-making, investment, action, and outcomes. The paper explains each of these three governance challenges, identifying possible avenues for addressing them, and highlights the importance of interlinkages between the three challenges.