  Precise tests of Lorentz invariance can be executed using neutrino
oscillations, which can provide sensitive measurements of suppressed signals of
new physics. This talk describes the neutrino sector of the Standard-Model
Extension, which represents a general modification of the Standard Model of
massive neutrinos to include Lorentz and CPT violation. Attainable
sensitivities as well as a framework to search for these violations are
presented for existing and future long-baseline neutrino experiments. The
applicability of this framework to short-baseline experiments is also
discussed.
