The momentum distribution of the protons participating in hydrogen bonds in water and ice deviates considerably from the classical equilibrium distribution. As a consequence the molecular structure of water and ice is directly affected by quantum mechanics. Yet the effect is essentially quasi-harmonic and quasi-classical in nature. New physics occurs in presence of proton tunneling, which is collective and dominated by strong local correlations. These effects will be discussed with special reference to the transition from ice VIII to ice VII, which is driven by quantum fluctuations under appropriate temperature an d pressure conditions.