Searches for rare and Beyond the Standard Model processes in top quark production and decays with the CMS experiement

With millions of top quarks produced at the LHC, it is an ideal sector for searching for rare top-quark decays. Besides flavor-changing neutral currents that are highly suppressed in the Standard Model, baryon and lepton number conservation can be probed in top quark events. In this conference proceeding, recent searches by the CMS experiment for rare and beyond the Standard Model top-quark production and decay with significantly increased sensitivity are discussed. Several of the measurements are the first of their kind.