Several use cases already proposed for 5G networks cannot be facilitated by terrestrial infrastructure, either due to its small penetration in remote/rural areas or the harsh propagation conditions due to the terrain. Indicative applications include forestry, mining, agriculture, semi-autonomous control of long-range vehicles, industrial services, logistics, asset tracking, telemedicine, beyond visual-line-of-sight drone operations, and maritime insurance. Hence, such use cases necessitate the integration of terrestrial with non-terrestrial networks, which gives rise to several challenges to overcome. The project ETHER aims to provide a holistic approach for energy- and cost-efficient integrated terrestrialnon-terrestrial networks. To achieve this goal, ETHER develops solutions for a unified Radio Access Network and for Artificial Intelligence-enabled resource management across the terrestrial, aerial, and space domains while creating the business plans driving future investments. To that end, this paper discusses a series of key technologies that ETHER combines under a unique 3-Dimensional (3D) multi-layered architectural proposition that brings together: i) user terminal antenna design and implementation for direct handheld access in the integrated network, ii) a robust unified waveform, iii) energy-efficient seamless horizontal and vertical handover policies, iv) a zero-touch network/service management and orchestration framework, v) a flexible payload system to enable programmability in the aerial and space layers, vi) joint communication, compute, and storage resource allocation solutions targeting at end-to-end network performance optimisation leveraging novel predictive analytics, and vii) energy-efficient semantics-aware information handling techniques combined with edge computing and caching for reduced latency across the distributed 3D compute/storage continuum. The 3D ETHER architecture and the targeted use cases are also discussed, paving the way toward 6G networks.