By combining molecular dynamics (MD) simulations with Si-29 and Al-27 magic-angle spinning nuclear magnetic resonance (NMR) spectroscopy, we present a comprehensive structural report on rare-earth (RE) aluminosilicate (AS) glasses of the RE2O3-Al2O3-SiO2 (RE = Y, Lu) systems, where the latter is studied for the first time. The structural variations stemming from changes in the glass composition within each RE system as well as the effects of the increased cation field-strength (CFS) of Lu3+ relative to Y3+-are explored and correlated to measured physical properties, such as density, molar volume, glass transition temperature, and Vickers hardness (H-V). Si-29 NMR reveals a pronounced network ordering for an increase in either the RE or Al content of the glass. Al mainly assumes tetrahedral coordination, but significant AlO5 and AlO6 populations are present in all structures, with elevated amounts in the Lu-bearing glasses compared to their Y analogues. The MD-derived oxygen speciation comprises up to 3% of free O2- ions, as well as non-negligible amounts (4-19%) of O-[3] coordinations ("oxygen triclusters"). While the SiO4 groups mainly accommodate the nonbridging oxygen ions, a significant fraction thereof is located at the AlO4 tetrahedra, in contrast to the scenario of analogous alkali- and alkaline-earth metal-based AS glasses. The average coordination numbers (CNs) of Al and RE progressively increase for decreasing Si content of the glass, with the average CN of the RE3+ ions depending linearly on both the amount of Si and the fraction of AlO5 groups in the structure. The Vickers hardness correlates strongly with the average CN of Al, in turn dictated by the CFS and content of the RE3+ ions. This is to our knowledge the first structural rationalization of the well-known compositional dependence of H-V in RE bearing AS glasses.