Environmental, social and economic challenges antagonize sustainable development. Understanding the emergent collective dynamics of the underlying complex interconnected systems is key to predicting processes and preventing failures. This requires integrating data-driven methods, computational modeling and conceptual theoretical progress as well as specific insights from a variety of different fields. Here we review recent advances in analyzing collective dynamics of infrastructure systems, focusing on electric energy supply and sustainable mobility. Key phenomena include flow disruptions, supply fluctuations and non-equilibrium states emerging through distributed demand—highlighting the need for cross-disciplinary tools to guide sustainable system design.