A broad and general search for Lorentz violation across all of physics has been in progress for the past several decades. The primary motivation is to search for a signal of new physics, possibly originating at the Planck scale. This talk will review the structure of the gravitational Standard-Model Extension framework for systematically searching for Lorentz violation, then narrow to recent efforts in gravitational physics. Proposals and tests involving systems such as gravitational wave propagation, the MICROSCOPE equivalence-principle mission, and Sagnac gyroscopes will be discussed.