Information and communication technology (ICT) offers promising opportunities to address global sustainability challenges such as climate change and social inequality by enabling energy savings and social innovations. At the same time, ICT threatens to exacerbate these crises, as evident in the increasing consumption of resources and widening digital inequalities. As one of the enablers of ICT, software engineering plays a key role to tackle the problems and explore the potentials of ICT for sustainability. However, sustainability in software engineering is still a niche topic, with little structure, a limited understanding of sustainability and few comprehensive strategies. In this article, we introduce the main concepts of Sustainable Software Engineering, critically review the state of research and identify seven future research challenges across all research areas. We further present our research vision—sustainability-driven software engineering and transdisciplinary research formats—and outline a research roadmap with the key steps to be achieved by 2030.