In the last 50 years we have seen how an initially ad-hoc and not widely accepted theory of the strong and electroweak interactions (Standard Theory: ST) has correctly predicted the entire accelerator based experimental observations with incredible accuracy (with the important exception of neutrino oscillation experiments). Decays of the ST particles (quarks and leptons), which are rare due to some symmetry of the theory, have played an important role in the formalism of the ST. These rare decays have been powerful tools to search for new particle interactions with the ST particles, which may not necessarily have the same symmetries. In this article, I will describe the indirect search for evidence of new physics (NP) using quark and lepton flavour changing neutral decays, which are highly suppressed within the ST, and constitute strong probes of potential new flavour structures.