Rare Gases (RG=He, Ne, Ar, Kr, Xe) are ubiquitous in Earth, solar system planets, stars and interstellar medium so understanding them is necessary to understand the composition and evolution of the universe. From a technological point of view RGs are also important because they present remarkable mechanical and reactivity properties that have been exploited in hydrostatic pressure-transmitter medium applications in high-pressure experiments and synthesis processes. At normal P-T conditions, RGs are considered among the most simple systems because they posses closed-shell electronic structure which prevent them from reacting with other atomic species and conducting electricity. Nevertheless, in both low P-T and high P-T regimes RGs exhibit very intriguing behaviour which defies and challenges both classical and modern physics conceptions [1]. In this talk, I will review recent theoretical work done on He and RG-He mixtures under pressure [2,3]. Key ideas of the computational approaches used on these investigations, namely density functional theory (DFT) and the diffusion Monte Carlo method (DMC), will be also highlighted. In particular, I will talk about the phase diagram and physical properties of Ne(He)2, a compound which is observed to stabilize in the MgZn2 Laves structure at low P and for which we recently have predicted a series of solid-solid phase transitions induced by effect of pressure. We also have conducted investigations on the Ar(H2)2 system [4] where it has been suggested possible chemical-induced metallization of hydrogen at compressions already within the reach of present diamond-anvill-cell (DAC) facilities (P~175GPa). Interestingly, based on preliminary DFT and ab initio molecular dynamics results, we predict a new solid-solid phase boundary on the phase diagram of this compound and unravel a novel type of melting behaviour at extreme P-T conditions [1] C. Cazorla et al., New J. of Phys. 11, 013047 (2009) [2] C. Cazorla and J. Boronat, J. of Phys.: Condens. Matt. 20, 015223 (2008) [3] C. Cazorla, D. Errandonea and E. Sola, Phys. Rev. B 80, 064105 (2009) [4] C. Cazorla and D. Errandonea, to be published