The incorporation of rare-earth (RE) elements into an aluminosilicate (AS) glass generally enhances its optical and mechanical properties. Atomistic molecular dynamics (MD) simulations were employed for probing the coordinations of Y3+ and Sc3+ in Y2O3-Al2O3-SiO2 and Sc2O3-Al2O3-SiO2 glasses of variable Si, Al, and RE contents. YO6 and ScO5 polyhedra are the most abundant RE species. We explore the trends in the distributions of the various (non)bridging oxygen species and Si/Al/RE cations in the first and second RE coordination spheres, respectively. The lowest REM and R051 coordinations of both Y and Sc exhibit a strong preference for coordinating non-bridging 0 species, which gradually relaxes for increasing coordination number p. Clear deviations from a statistical Si/AI/RE distribution around the REOp polyhedra is observed, with preferences for RE-RE contacts relative to RE-Al and (notably) RE-Si. The extents of RE-RE associations are similar for Y and Sc and grow slightly for increasing Si content and/or glass network polymerization. The propensity for RE-Al contacts becomes emphasized in the Sc AS glasses, mainly at the expense of Sc-Si. The YOp and ScOp polyhedra connect to their Si/Al/RE neighbors primarily by sharing corners, but a significant extent of edge-sharing is also observed, which increases both with the RE1PI coordination number, and along the series Si < Al-[4] < Al-[5]/Al-[6] approximate to RE of neighbors.