The search for Flavour Changing Neutral Current (FCNC) processes constitutes an important research topic at the LHC. Forbidden at tree level and highly suppressed at higher orders in the Standard Model, FCNC processes can present enhanced contributions in many extensions of the Standard Model. Therefore, such processes become particularly attractive for probing New Physics in the top-quark sector, where searches for top-quark anomalous couplings offer complementarity to the searches for new heavy resonances which have not yet been successful. In this context, a comprehensive high-precision search for FCNC processes in both top-quark production and decay is pursued with the ATLAS experiment. This seminar presents the status of this research activity.