ttX and top properties in ATLAS and CMS

The top quark offers a very rich physics program. This talk focuses on searches for flavor-changing neutral-current (FCNC) and on measurements and searches for rare top production modes, the so called ttX processes. FCNC couplings are strongly suppressed in the standard model (SM) but included in many extensions of the SM. The ttX processes become fully accessible with the Run 2 data inclusively and differentially and first searches are carried out within the framework of an effective field theory. The measurements and searches presented are performed with the full Run 2 data of the CERN Large Hadron Collider (LHC) at a center-of-mass of 13~TeV with the ATLAS [1] and CMS experiments [2].