The contributions in this theme issue of Philosophical Transactions of the Royal Society A address important global trends in energy management, both current and anticipated. Particularly in the context of electrical power systems, these trends will present complex scientific challenges in decision analysis and optimization, in the analysis and assessment of risk and in the modelling of flexibility, and will raise numerous computational issues. The articles herein aim to suggest new ways in which engineering and mathematics can combine to address them. Significant challenges arise from the increasing connection of variable renewable energy generation. Despite their long-term benefits in terms of sustainability, renewable resources such as solar and wind power are both highly variable and partially unpredictable. They, therefore, present operational challenges in assessing and mitigating risk, including issues of imbalance between generation and demand and network constraints. Additionally, there is longer term uncertainty over the technology costs and environmental policies associated with renewable generation, among other factors. These uncertainties at various time scales may imply the need for significant investment in new, more flexible ‘smart grid’ technologies capable of adaptation to a range of future scenarios. As laid out in [1], examples are Particularly in the presence of uncertainty, such flexible technologies present a variety of new analytical challenges relating to short- and long-term decision-making. Owing to the scale and complexity of electrical power systems, models of their flexible operation under uncertainty may be both difficult to formulate and computationally expensive to evaluate. While on longer time scales, the issue of computational speed is less acute, new …