  We survey the flavor-changing neutral couplings (FCNC) of the top quark
predicted by some extensions of the Standard Model: THDM, SUSY, L-R symmetric,
TC2, 331, and models with extra quarks. Since the expected sensitivity of the
LHC and ILC for the tcV (V=\gamma,g,Z) and tcH couplings is of order of a few
percent, we emphasize the importance of any new physics effect that gives a
prediction for these FCNC couplings within this limit. We also review the
constraints imposed on these couplings from low-energy precision measurements.
