  The quark sector of the Standard Model exhibits an approximate U(2)^3 flavour
symmetry. This symmetry, broken in specific directions dictated by minimality,
can explain the success of the Cabibbo-Kobayashi-Maskawa picture of flavour
mixing and CP violation, confirmed by the data so far, while allowing for
observable deviations from it, as expected in most models of ElectroWeak
Symmetry Breaking. Building on previous work in the specific context of
supersymmetry, we analyze the expected effects and we quantify the current
bounds in a general Effective Field Theory framework. As a further relevant
example we then show how the U(2)^3 symmetry and its breaking can be
implemented in a generic composite Higgs model and we make a first analysis of
its peculiar consequences. We also discuss how some partial extension of U(2)^3
to the lepton sector can arise, both in general and in composite Higgs models.
An optimistic though conceivable interpretation of the considerations developed
in this paper gives reasons to think that new physics searches in the flavour
sector may be about to explore an interesting realm of phenomena.
