  This paper is based on the invited talks delivered by the author at GR 19:
the 19th International Conference on General Relativity and Gravitation, Ciudad
de M\'exico, M\'exico, July 2010. In Part 1, we briefly review some of the main
features of quantum gravity with anisotropic scaling, and comment on its
possible relation to the causal dynamical triangulations (CDT) approach to
lattice quantum gravity. Part 2 explains the construction of gravity with
anisotropic scaling with an extended gauge symmetry -- essentially a
nonrelativistic version of general covariance. This extra symmetry eliminates
the scalar graviton polarization, and thus brings the theory closer to general
relativity at long distances.
