ExaNest is one of three European projects that support a ground-breaking computing architecture for exascale-class systems built upon power-efficient 64-bit ARM processors. This group of projects share an "everything-close" and "share-anything" paradigm, which trims down the power consumption -- by shortening the distance of signals for most data transfers -- as well as the cost and footprint area of the installation -- by reducing the number of devices needed to meet performance targets. In ExaNeSt, we will design and implement: (i) a physical rack prototype and its liquid-cooling subsystem providing ultra-dense compute packaging, (ii) a storage architecture with distributed (in-node) non-volatile memory (NVM) devices, (iii) a unified, low-latency interconnect, designed to efficiently uphold desired Quality-of-Service guarantees for a mix of storage with inter-processor flows, and (iv) efficient rack-level memory sharing, where each page is cacheable at only a single node. Our target is to test alternative storage and interconnect options on actual hardware, using real-world HPC applications. The ExaNeSt consortium brings together technology, skills, and knowledge across the entire value chain, from computing IP, packaging, and system deployment, all the way up to operating systems, storage, HPC, big data frameworks, and cutting-edge applications.