  S3 models offer a low energy approach to describe the observed pattern of
masses and mixing, of both quarks and leptons. In this work, we first revisit
an S3 model with only one Higgs electroweak doublet, where the flavour symmetry
must be broken in order to produce an acceptable pattern of masses and mixing
for fermions. Then, we analyse different S3 models, where the flavour symmetry
is preserved as an exact, but hidden symmetry of the low energy spectra, after
the electroweak symmetry breaking. The latter models require the addition of
two more Higgs electroweak doublets which are accommodated in an S3 doublet. We
also explore the consequences of adding a fourth Higgs electroweak doublet,
thus occupying all three irreducible representations of S3. We show how the
various S3-invariant mass matrices of the different models can reproduce the
two texture zeroes and Nearest Neighbour Interaction matrix forms, which have
been found to provide a viable and universal treatment of mixing for both
quarks and leptons. We also find analytical and exact expressions for the CKM
matrix of the models in terms of quark mass ratios. Finally, we compare the
expressions of the CKM matrix of the different S3 models with the most up to
date values of masses and mixing in the quark sector, via a chi^2 analysis. We
find that the analytical expressions we derived reproduce remarkably well the
most recent experimental data of the CKM matrix, suggesting that S3 is a
symmetry of the quark sector.
