Urban environments are expected to accrue most population and economic growth worldwide going forward. Cities are also environments where sustainability plans aimed at the decarbonization of the energy supply must be made compatible with goals of human development and equity. In this talk, I will present two recent papers that address these convergent issues. The first deals with the shape of the built environment of US cities, and constitutes the largest analyses of 3D urban models to date. I will show how urban built form changes systematically with city size, and how this change generates unintended positive outcomes in terms of energy savings in transportation and climate control. In the second, I will show how the built environment of all cities is being mapped to unprecedented precision through a mixture of remote sensing, community organization, novel technologies and official statistics. This information allows us to appreciate many adaptive forms of energy use in cities and strong distributional effects in urban services. I will show how a systematic mathematical analysis of built environments becomes possible and enable new models of urban planning and policy. I will wrap up with some comments about the Mansueto Institute for Urban Innovation, highlight a couple of its initiatives and opportunities for collaboration across the University.