The importance of being discrete Balder ten Cate, Tadeusz Litak Abstract: The paper discusses discrete frames as an attractive semantics for modal logic. We study questions of completeness, persistence, duality and definability. Notions of completeness, strong global completeness and complexity of dual varieties coincide for discrete frames; moreover, they are equivalent to conservativity of minimal hybrid extensions. The paper also provides some criteria of di-persistence and a Goldblatt-Thomason theorem for discrete frames.