I will review the recent proposal to make general relativity renormalizable in 4D at the expense of breaking Lorentz invariance. After introducing the original idea by P. Horava through a toy model, I will present the similar realization for the gravitational field where an extra degree of freedom with respect to general relativity will appear. Depending on the behavior of the extra mode, the theory may become unstable or strongly coupled. As I will show, there is still a window in parameter space without any of these blatant problems and compatible with the first phenomenological tests.