It has been known since the pioneering work of Bernal, Fowler and Pauling that hexagonal water ice is the architype of a frustrated material : a proton-bonded network in which protons satisfy strong local constraints - the "ice rules" - but do not order.

Frustration of this type has been rediscovered many times since, in the context of charge order on pyrochlore lattice, proton-bonded ferroelectrics, models of polymer melts and, most famously, the family rare earth pyrochlore oxides known as "spin ice" - prime examples of materials with strong spin-orbit coupling.

Recently "quantum spin-ice" materials have attracted considerable attention as potential hosts for a quantum spin-liquid, in which the collective excitations of spins are described by a U(1) lattice gauge theory, and have the character of photons.

In this talk we review some of the theoretical progress in understanding quantum spin ice, with emphasis on recent numerical results, and pose the question : should we be looking for a similar quantum liquid in the protons of water ice?

[1] O. Benton, O. Sikora and N. Shannon, arXiv:1504.04158