FCNC top quark decays beyond the Standard Model

Flavor Changing Neutral Current decays of the top quark within the strict context of the Standard Model are known to be extremely rare. In fact, they are hopelessly undetectable at the Tevatron, LHC and LC in any of their scheduled upgradings. Therefore, if a few of these events eventually show up in the future we will have certainly discovered new physics. We argue that this could well be the case for the LHC and the LC both within the Minimal Supersymmetric Standard Model (MSSM) and in a general two-Higgs-doublet model (2HDM), especially if we look for FCNC top quark decays into Higgs bosons.