  Minimal Flavour Violation (MFV) postulates that the only source of flavour
changing neutral currents and CP violation, as in the Standard Model, is the
CKM matrix. However it does not address the origin of fermion masses and mixing
and models that do usually have a structure that goes well beyond the MFV
framework. In this paper we compare the MFV predictions with those obtained in
models based on spontaneously broken (horizontal) family symmetries, both
Abelian and non-Abelian. The generic suppression of flavour changing processes
in these models turns out to be weaker than in the MFV hypothesis. Despite
this, in the supersymmetric case, the suppression may still be consistent with
a solution to the hierarchy problem, with masses of superpartners below 1 TeV.
A comparison of FCNC and CP violation in processes involving a variety of
different family quantum numbers should be able to distinguish between various
family symmetry models and models satisfying the MFV hypothesis.
