  In this proceedings, I summarize two recently discovered theoretical
implications that Lorentz violation has on physical systems. First, I discuss
new models for neutrino oscillations in which relatively simple combinations of
Lorentz-violating parameters can mimic the major features of the current
neutrino oscillation data. Second, I will present results on Yang-Mills
instantons in Lorentz-violating background fields. An explicit solution is
presented for unit winding number in SU(2).
