For any fundamental local quantum field theory, unitarity, renormalizability, and relativ-istic invariance are considered to be essential properties. Unitarity is inevitably connect-ed to the probabilistic interpretation of the quantum theory, while renormalizability guar-antees its completeness. Relativistic invariance, in turn, is a symmetry which derives from the structure of spacetime. So far, any perturbative attempt to formulate a funda-mental quantum field theory of gravity seems to be in conflict with at least one of these three properties. In quantum Lifshitz theories -- quantum field theories with an aniso-tropic scaling between space and time -- unitarity and renormalizability can be retained while Lorentz invariance is sacrificed and only emerges as approximate symmetry at low energies. I discuss several advancements towards the construction of a unitary and renormalizable quantum Lifshitz theory of gravity.