The Lassoing Rhetoric venture is interesting for its multifaceted approach to linguistic devices, prominently including rhetorical figures, but also RST relations and stylistic models, like the use of historic present. We include ontological models of argument schemes applying Rhetorical Structure Theory (RST) the RhetFig proposal for modeling the related RetFig Ontology of Rhetorical Figures for Serbian (developed by two of the authors) and the Lassoing Rhetoric project (developed by another of the authors). This paper surveys ontological modeling of rhetorical concepts, developed for use in argument mining and other applications of computational rhetoric, projecting their future directions.