By connecting digital models and physical assets in real time, digital twins enable new levels of agility across industry for planning and optimization, as well as predictive maintenance. The recent vision of Industry 5.0 puts digital twin technology at the service of the green transition, emphasizing sustainable and human-centric goals for industry. But in fact, these goals also concern nature and how humans interact with nature. In this talk, we explore the potential of digital twins as a technology backbone for Nature 5.0, connecting digital models with natural systems in real-time - not only for environmental monitoring, but for long-term decision making and sustainability. We discuss different aspects of engineering digital twins of ecosystems, including digital twin architectures, interoperability, model management, and self-adaptation, as well as challenges and opportunities in this interdisciplinary work. The talk will be illustrated by examples from our own work, such as the digital twin of the Oslofjord.