  The spin ice materials, including Ho2Ti2O7 and Dy2Ti2O7, are rare earth
pyrochlore magnets which, at low temperatures, enter a constrained paramagnetic
state with an emergent gauge freedom. Remarkably, the spin ices provide one of
very few experimentally realised examples of fractionalization because their
elementary excitations can be regarded as magnetic monopoles and, over some
temperature range, the spin ice materials are best described as liquids of
these emergent charges. In the presence of quantum fluctuations, one can
obtain, in principle, a quantum spin liquid descended from the classical spin
ice state characterised by emergent photon-like excitations. Whereas in
classical spin ices the excitations are akin to electrostatic charges, in the
quantum spin liquid these charges interact through a dynamic and emergent
electromagnetic field. In this review, we describe the latest developments in
the study of such a quantum spin ice, focussing on the spin liquid
phenomenology and the kinds of materials where such a phase might be found.
