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Flavour-Changing-Neutral-Currents (FCNC) play an important r\^ ole in testingthe Standard Model (SM) while probing the possibility of having New Physicsbeyond the SM. In the SM, FCNC are forbidden at three level, but arise throughcalculable one-loop contributions. We review some of the features of FCNC intwo examples of minimal extensions of the SM. In the first example, we consideran extension of the SM consisting of the addition of one vector-like quarkeither of the up-type ($Q=2/3$) or the down type ($Q=- 1/3$). In this extensionthere are non-vanishing but naturally suppressed Z-mediated FCNC at tree level.In the second example, we discuss extensions of the SM with two Higgs doublets,without the assumption of natural flavour conservation, giving rise to Higgsmediated FCNC. The existence of strict experimental limits on processessensitive to Higgs FCNC requires a strong suppression of these currents. Wepresent scenarios resulting from discrete symmetries where all new flavourstructures in the quark sector are parametrized by elements of theCabibbo-Kobayashi-Maskawa (CKM) matrix, together with the ratio of vacuumexpectation values of the Higgs doublets in the Higgs basis defined by thesymmetry. We extend these scenarios to the leptonic sector with thePontecorvo-Maki-Nakagawa-Sakata matrix playing a r\^ ole similar to the CKMmatrix in the quark sector.

New Physics in the Flavour Sector in the presence of Flavour Changing Neutral Currents