The uniform Sobolev estimate due to Kenig-Ruiz-Sogge (1987) is one of the (uniform) limiting absorption principle for the resolvent of the Laplacian and has played an important role in the study of spectral and scattering theory. It also has a close connection to global-in-time Kato-smoothing and Strichartz estimates for the free Schrödinger equation. In this talk, we discuss recent progress on its generalization to the Schrödinger operator with a class of scaling-critical real-valued potentials. Some applications to global-in-time Strichartz estimates and Hörmander's type multiplier theorem are also discussed.