Our research focuses on the extraordinary mechanics of slender large-span shells, membranes, and elastic rod networks under extreme loading and during construction. Our work concerns shape generation and analysis approaches for innovative lightweight structural systems that enable a resilient, and sustainable built environment. We focus on the advancement of theoretical and computational approaches to predict and design the overall properties, stability, and failure of these systems. Capturing the nonlinear behavior of these structures, especially those with complex geometries, spatially varying loading, and those undergoing large displacements or even large strains, can be challenging due to the inherent computational complexity of modeling these behaviors. Their design and associated loading conditions are also complex because of their spatial (1-1000m) and temporal (50-200 years) scales, and the challenge of materializing these systems over those scales. In terms of methodology development, we have been working on a comprehensive framework with advanced analytical formulations, numerical form finding and optimization approaches, fluid/structure interaction models, and machine-learning algorithms to open new avenues for accelerated discoveries and automated optimal designs. In terms of applications, we have used this framework to successfully innovate structural and architectural systems ranging from macro-scale adaptive shading devices to large-scale storm surge barriers. Large-span shells, membranes, and rod networks exhibit fascinating mechanical behaviors because geometric nonlinearities arise even when their material properties are linear. Their shape and topology give them properties beyond what is possible with conventional structural systems. In this paper, I outline how we discovered, studied, designed and even built large-scale structural surfaces that can efficiently carry extreme loading, self-assemble, adjust their stiffnesses, elastically shift from one shape to another, or amplify motion.