  CP violation plays a very important role in nature with implications both for
Particle Physics and for Cosmology. Accounting for the observed matter
anti-matter asymmetry of the Universe requires the existence of new sources of
CP violation beyond the Standard Model. In models with an extended scalar
sector CP violation can emerge either explicitly, i.e., at the Lagrangian
level, or spontaneously. In the context of multi-Higgs extensions of the
Standard Model imposing the existence of a scalar basis where all couplings are
real is a sufficient condition for CP to be explicitly conserved. We discuss a
three-Higgs-doublet model with an underlying $S_3$ symmetry, allowing in
principle for complex couplings. In this framework it is possible to have
either spontaneous or explicit CP violation in the scalar sector, depending on
the regions of parameter space corresponding to the different possible vacua of
the $S_3$ symmetric potential. We list all possible vacuum structures allowing
for CP violation in the scalar sector specifying whether it can be explicit or
spontaneous. It is by now established that CP is violated in the flavour sector
and that the Cabibbo-Kobayashi-Maskawa matrix is complex. In order to
understand what are the possible sources of CP violation in the Yukawa sector
we analyse the implications of the different available choices of
representations for the quarks under the $S_3$ group. This classification is
based strictly on the exact $S_3$-symmetric scalar potential with no soft
symmetry breaking terms. The scalar sector of one such model was explored
numerically. After applying the theoretical and the most important experimental
constraints the available parameter space is shown to be able to give rise to
light neutral scalars at the $\mathcal{O}(\text{MeV})$ scale.
