Lepton flavor violation (LFV) is one of the cleanest probes of physics beyond the standard model. After a brief review of the different experimental probes of LFV, I will discuss the special role of the process e+ e- -> tau mu in probing new physics. I will argue that searches for non-resonant e+ e- -> tau mu at high center-of-mass energies are highly complementary to other probes of LFV. I will show the results of our sensitivity studies for the FCC-ee and the CEPC, which indicate that these future colliders are competitive with the expected constraints from rare tau decays and Z decays.