  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.
