Rare top quark production and decays at ATLAS and CMS

The most recent studies in the top quark sector are reviewed with the focus on the rare production mechanisms and suppressed decays. The experimental results obtained with the ATLAS and CMS detectors in proton-proton collisions at the center-of-mass energy of 13 TeV include the measurements of the associated production of top quark pairs with vector bosons (${\rm t\bar{t}W}$, ${\rm t\bar{t}Z}$, ${\rm t\bar{t}\gamma}$), the first evidence for the ${\rm t(\bar{t})\gamma q}$ process, the first observation of the ${\rm t(\bar{t})Zq}$ production, the study of the ${\rm t\bar{t}+b\bar{b}}$ and ${\rm t\bar{t}+t\bar{t}}$ processes, as well as searches for lepton flavour violation in top quark decays and effective field theory interpretations. The experimental results show good agreement with the theoretical predictions.