Modern communication networks are rapidly evolving into sophisticated systems combining communication and computing capabilities. Computation at the network edge is the key to supporting many emerging applications, from extended reality to smart health, smart cities, smart factories and autonomous driving. SONATA is motivated by the fact that the large scale adoption of edge intelligence technology, while benefiting human productivity and efficiency, will result in a surge of data and computation in mobile networks, which, in turn, will exacerbate their already significant energy consumption. SONATA is an interdisciplinary effort to tame this growing energy demand by combining memristive hardware and energy harvesting technologies with novel machine learning algorithms and physical layer communication techniques. In particular, we want to combine the energy efficient in-memory computing and learning potential of memristive devices with an “over-the-air computation (OAC)” approach to edge learning, which turns the air from a purely communication medium to a computation unit. Our project not only aims at reducing the energy requirements of edge learning systems drastically, but also focuses on making them robust against stochastic failures, due to unreliable hardware or energy sources. We will exploit tools from circuit design, coding theory, wireless communications, machine learning and network science to achieve these goals. Results from SONATA will open up new directions for research and development of technologies that will allow mobile systems to offer the much anticipated communication and computing services in a sustainable manner.