On the Flavour Problems and Their Symmetry Solution(Particle Physics beyond the Standard Model)

After more than four decades of impressive and frustrating theoretical and experimental efforts to reveal signals of the presence of TeV new physics through its effects in CP conserving and CP violating flavour changing neutral current processes, the main response seems to lie in an effective flavour blindness of the new physics at the electroweak scale (Minimal Flavour Violation). This perspective keeps still open the door for main surprises in the sector of lepton flavor violation. Here we explore, together with other participants in the YKIS symposium at the Yukawa Institute, an alternative road where both the flavour puzzle within the Standard Model (i.e., a rationale for the smallness of Yukawa couplings and fermion mixings) and the flavour problem of TeV new physics are simultaneously tackled in a Supersymmetric extension of the Standard Model where the flavour structure is dictated by a (spontaneously broken) flavour or horizontal symmetry. I will discuss the main relevant implications of such class of models for both the leptonic and hadronic rare flavour changing processes.