We have carried out a comprehensive first-principles study of the energetic, structural, and electronic properties of solid rare-gas ͑RG͒-helium binary compounds, in particular, Ne͑He͒ 2 and Ar͑He͒ 2 , under pressure and at temperatures within the range of 0 Յ T Յ 2000 K. Our approach is based on density-functional theory and the generalized gradient approximation for the exchange-correlation energy; we rely on total Helmholtz freeenergy calculations performed within the quasiharmonic approximation for most of our analysis. In Ne͑He͒ 2 , we find that at pressures of around 20 GPa the system stabilizes in the MgZn 2 Laves structure, in accordance to what was suggested in previous experimental investigations. In the same compound, we predict a solid-solid phase transition among structures of the Laves family of the type MgZn 2 → MgCu 2 , at a pressure of P t = 120͑1͒ GPa. In Ar͑He͒ 2 , we find that the system stabilizes in the MgCu 2 Laves phase at low pressures but it transitates toward the AlB 2 -type structure by effect of compression at P t = 13.8͑4͒ GPa. The phonon spectra of the Ne͑He͒ 2 crystal in the MgZn 2 and MgCu 2 Laves structures, and that of Ar͑He͒ 2 in the AlB 2 -type phase, are reported. We observe that the compressibility of RG-RG and He-He bond distances in RG͑He͒ 2 crystals is practically identical to that found in respective RG and He pure solids. This behavior emulates that of a system of noninteracting hard spheres in closed-packed configuration and comes to show the relevance of short-range interactions on this type of mixtures. Based on size-ratio arguments and empirical observations, we construct a generalized phase diagram for all RG͑He͒ 2 crystals up to a pressure of 200 GPa where we map out systematic structural trends. Excellent qualitative agreement between such generalized phase diagram and accurate ab initio calculations is proved. A similar construction is done for RG͑H 2 ͒ 2 crystals; we find that the MgCu 2 Laves structure, which has been ignored in all RG-H 2 works so far, might turn out to be competitive with respect to the MgZn 2 and AlB 2 -type structures. Furthermore, we explore the pressure evolution of the energy-band gap in RG͑He͒ 2 solids and elaborate an argument based on electronic-band theory which explains the observed trends.