Abstract The concept of “ideal semantics” has been promoted as an alternative basis for skeptical reasoning within abstract argumentation settings. Informally, ideal acceptance not only requires an argument to be skeptically accepted in the traditional sense but further insists that the argument is in an admissible set all of whose arguments are also skeptically accepted. The original proposal was couched in terms of the so-called preferred semantics for abstract argumentation. We argue, in this paper, that the notion of “ideal acceptability” is applicable to arbitrary semantics and justify this claim by showing that standard properties of classical ideal semantics, e.g. unique status, continue to hold in any “reasonable” extension-based semantics. We categorise the relationship between the divers concepts of “ideal extension wrt semantics ?” that arise and we present a comprehensive analysis of algorithmic and complexity-theoretic issues.