In this talk I will discuss solutions of type IIB supergravity with an isometry group of non-relativistic scaling symmetry and in a special case, the well-known Schrodinger symmetry. In particular I will discuss supersymmetric backgrounds with Schrodinger isometry and renormalization group flow geometries with Schrodinger isometry at the fixed points. I will also discuss more general scale-invariant gravity backgrounds characterized by a general dynamical exponent. This talk is based on: arXiV:0904.2873 [hep-th], arXiV:0905.0673 [hep-th] and work in progress.