The nature of invisible dark matter (DM), which constitutes ~26% of the mass-energy balance of the Universe, remains a major puzzle in physics. Despite extensive searches, DM constituents remain undetected, though experiments have significantly constrained the allowed parameter space. The NEXUS project aims to advance this research by enhancing detector performance, refining instrumentation, and expanding theoretical insights through a sustainable expert network. Partnering with world-class laboratories in Europe, the USA, Canada, Australia, and South Africa, NEXUS will tackle extraordinary experimental and theoretical challenges. This research relies on Underground Laboratories (ULs), where cosmic rays are suppressed by ~1000 meters of rock, minimizing the cosmogenic backgrounds. The proposed NEXUS initiative aims to establish a global network of ULs dedicated to ground-breaking advancements in the field. The collaborative approach undertaken in NEXUS is designed to provide a dynamic environment for advances in ultra-sensitive detectors and ultra-low radiation techniques, ready to lead innovation in both the global search for rare events and cutting-edge technological development ultimately benefiting society and industry. ULs’ support for research will provide: (i) effective radiation shielding; (ii) above-ground and underground support facilities, such as clean (radon-free) rooms, radio-purity assay equipment, and cryogenic equipment; (iii) material production and purification facilities; (iv) tools and methods to characterize underground facilities and related instrumentation; and (v) a unique environment for multidisciplinary research. In addition, efforts are being made to further increase instrument sensitivity to meet new challenges in rare-event research. NEXUS will pave the way for ground-breaking discoveries, fostering a deeper understanding of the universe while driving technological advancements with broad societal and industrial benefits.