The very new evolution towards 6G networks necessitates a paradigm shift towards unified 3D network architectures, encompassing space, air, and ground segments. This paper outlines the conceptualization, challenges, and prospects of such a transformative architecture. We outline the foundational principles, drawn from standardization endeavors and cutting-edge research initiatives, to articulate the envisioned architecture poised to redefine network capabilities. Driven by the need to enhance capacity, increase data rates, support diverse mobility models, and facilitate heterogeneous connectivity, the conceptual framework of a unified 3D network is presented. The focus is on seamlessly integrating diverse network segments and fostering holistic network orchestration. In examining the technical challenges inherent to the realization of a unified 3D network, we outline our strategies to address mobility management, handover optimization, interference mitigation, and the integration of distributed physical layer concepts. Proposals encompass federated learning mechanisms, advanced beamforming techniques, and energy-efficient computational offloading strategies, aimed at enhancing network performance and resilience. Moreover, we outline compelling utilization scenarios and highlighted promising avenues for future research.