  Flavour-Changing-Neutral-Currents (FCNC) play an important r\^ ole in testing
the Standard Model (SM) while probing the possibility of having New Physics
beyond the SM. In the SM, FCNC are forbidden at three level, but arise through
calculable one-loop contributions. We review some of the features of FCNC in
two examples of minimal extensions of the SM. In the first example, we consider
an extension of the SM consisting of the addition of one vector-like quark
either of the up-type ($Q=2/3$) or the down type ($Q=- 1/3$). In this extension
there 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 Higgs
mediated FCNC. The existence of strict experimental limits on processes
sensitive to Higgs FCNC requires a strong suppression of these currents. We
present scenarios resulting from discrete symmetries where all new flavour
structures in the quark sector are parametrized by elements of the
Cabibbo-Kobayashi-Maskawa (CKM) matrix, together with the ratio of vacuum
expectation values of the Higgs doublets in the Higgs basis defined by the
symmetry. We extend these scenarios to the leptonic sector with the
Pontecorvo-Maki-Nakagawa-Sakata matrix playing a r\^ ole similar to the CKM
matrix in the quark sector.
