$S_3$ as a unified family theory for quarks and leptons

We present an $S_3$-invariant extension of the SM which is able to account for the mixing both in the quark and the lepton sector. We focus here on the quark sector and present different realizations of the model, according to how many Higgs fields are involved. We then confront the models with the up-to-date values of masses and mixing in the quark sector.