Recent work has highlighted remarkable effects of classical thermal
fluctuations in the dipolar spin ice compounds, such as "artificial
magnetostatics", manifesting as Coulombic power-law spin correlations and
particles behaving as diffusive "magnetic monopoles". In this paper, we address
quantum spin ice, giving a unifying framework for the study of magnetism of a
large class of magnetic compounds with the pyrochlore structure, and in
particular discuss Yb2Ti2O7 and extract its full set of Hamiltonian parameters
from high field inelastic neutron scattering experiments. We show that
fluctuations in Yb2Ti2O7 are strong, and that the Hamiltonian may support a
Coulombic "Quantum Spin Liquid" ground state in low field and host an unusual
quantum critical point at larger fields. This appears consistent with puzzling
features in prior experiments on Yb2Ti2O7. Thus Yb2Ti2O7 is the first quantum
spin liquid candidate in which the Hamiltonian is quantitatively known.