Monte-Carlo modeling in single top quark and in other rare top-related processes

The production of top quarks through single or rare production modes has become important due large amount of data collected by both ATLAS and CMS. Many searches are now studying these processes either as a targeted signal or as an important source of background. This document will review how the Monte Carlo simulations are used to simulate these processes in ATLAS and CMS, and how the modelling systematic uncertainties are estimated. Many analyses have also recently released a large variety of unfolded distributions. This distributions will be shown and the modelling from various Monte Carlo generators will be compared to the data.