Models are increasingly used to inform the transformation of human-natural systems towards more sustainable futures, aligned with the United Nations Sustainable Development Goals (SDGs). However, the future uncertainty of alternative socioeconomic and climatic scenarios challenges the model-based analysis of sustainable development. Obtaining robust insights, which can remain valid under many plausible futures, requires a systematic processing of uncertainty through scenario modelling. Here, we use exploratory modelling—an approach for exploring the implications of various modelling assumptions using computational experiments—to quantify and analyse the impacts of global socioeconomic and climate uncertainties in achieving SDGs. We develop a systematic, computational methodology to guide researchers in coping with future uncertainty in sustainable development, consistent with global benchmark scenario frameworks. To demonstrate, we implement the global climate and sustainability scenarios, namely the Shared Socioeconomic Pathways and the Representative Concentration Pathways, in an integrated assessment model for evaluating the global trajectories of eight SDGs related to sustainable food and agriculture, health and well-being, quality education, clean energy, sustainable economic growth, climate action, and biodiversity conservation under uncertainty. The results show that the progress towards different goals is highly sensitive to the modelled scenarios and to their uncertainty specification. This sensitivity highlights the importance of enumerating the diversity of alternative scenarios and their uncertainty exploration to enable a comprehensive assessment of sustainable development with the consideration of performance across a range of plausible futures and their boundary conditions. The enhanced modelling of scenarios can help prepare for a wider variety of future possibilities in planning for sustainability.