We present a first principles theoretical framework that accurately accounts for several properties of ice, over a wide pressure range. In particular, we show that, by using a recently developed nonlocal van der Waals functional and by taking into account hydrogen zero point motion, one can properly describe the zero temperature equation of state, the vibrational spectra, and the dielectric properties of ice at low pressure and of ice VIII, a stable phase between 2 and 60 GPa. While semilocal density functionals yield a transition pressure from ice XI to VIII that is overestimated by almost an order of magnitude, we find good agreement with experiments when dispersion forces are taken into account. Zero point energy contributions do not alter the computed transition pressure, but they affect structural properties, including equilibrium volumes and bulk moduli.