Results from extensive abinitio calculations for hydrogen, helium and their mixtures at high pressures are reported. For H, special attention has been paid to the nonmetal-to-metal-transition and its accompanying first-order liquid-liquid phase transition. Furthermore, an accurate wide range EOS is calculated for He, which is of paramount interest for interior structure models of giant planets and brown dwarfs. A high pressure phase diagram of He is derived. Finally, the miscibility gap of H and He is calculated and its implication for the structure and evolution of giant planets is discussed.