Searches for flavour changing neutral currents in the top sector

Flavour Changing Neutral Current (FCNC) processes are forbidden at tree level in the Standard Model and highly suppressed at higher orders. This makes FCNC one of the key processes to search for new physics since any small deviations from the Standard Model expectations could have a big impact. Both ATLAS and CMS Collaborations have designed a comprehensive strategy to search for FCNC in top quark physics both in the production and decay. The strategies followed by both collaborations are here described, using data from $pp$ collisions at the LHC collected at a centre of mass energies of 7 and 8~TeV with integrated luminosities ranging from $5~\rm{ fb}^{-1}$ to $20.3~\rm{ fb}^{-1}$.