The large integrated luminosity collected by the ATLAS detector during Run 2 of the LHC provides a huge sample of top quark physics events in which to study rare Standard Model (SM) processes and probe for the presence of new physics. New couplings beyond the SM (BSM) could enhance the rate of very rare top quark processes providing sensitivity for flavour-changing neutral current (FCNC) or lepton flavour-violating (LFV) interactions of the top quark. In the SM, both FCNC and LFV interactions involving the top quark are so small that any significant measurable cross-section for such a process is an indication of new physics. The ATLAS experiment has recently reported the observation of the rare SM 4-top production process which is sensitive to new physics. Additionally, dedicated searches have been performed for FCNC couplings of the top quark with a photon, gluon, Z boson or Higgs boson, as well as LFV couplings to another up-type quark, a muon and a tau lepton. In this seminar the most recent results will be presented and the experimental challenges and systematic uncertainties will be discussed.