Energy economy models are central to decision making on energy and climate issues in the 21st century, such as informing the design of deep decarbonisation strategies under the Paris Agreement. Designing policies that are aimed at achieving such radical transitions in the energy system will require ever more in-depth modelling of end-use demand, efficiency and fuel switching, as well as an increasing need for regional, sectoral, and agent disaggregation to capture technological, jurisdictional and policy detail. Building and using these models entails complex trade-offs between the level of detail, the size of the system boundary, and the available computing resources. The availability of data to characterise key energy system sectors and interactions is also a key driver of model structure and parameterisation, and there are many blind spots and design compromises that are caused by data scarcity. We may soon, however, live in a world of data abundance, potentially enabling previously impossible levels of resolution and coverage in energy economy models. But while big data concepts and platforms have already begun to be used in a number of selected energy research applications, their potential to improve or even completely revolutionise energy economy modelling has been almost completely overlooked in the existing literature. In this paper, we explore the challenges and possibilities of this emerging frontier. We identify critical gaps and opportunities for the field, as well as developing foundational concepts for guiding the future application of big data to energy economy modelling, with reference to the existing literature on decision making under uncertainty, scenario analysis and the philosophy of science.