In this volume, seven experts in logic and semantics examine reasons for using the intensional operator approach over the variable binding approach and vice versa. In logic and semantics there are two alternative tools that can be applied to many types of embedding phrases (modal, temporal, etc): the intensional operator approach and the variable binding approach. A rivalry between operators and quantifiers occurs in many areas of semantics: e.g. tense, modality, locational operators, epistemic modality. There are areas where the operator approach dominates, and areas where quantifiers prevail. Sometimes, as in the case of tense, roles have switched, and where one approach used to dominate, the other has taken over. This volume features contributions from leading experts in the field that examine the following questions: what exactly is at stake in a choice between the alternatives? are there any principled reasons for deciding which approach to use in which case? should we be purists and eliminate one approach completely in favour of the other? Operators vs Quantifiers will be a key resource for academics, researchers, and advanced students of philosophy, linguistics, computer science and mathematics. This book was originally published as a special issue of Inquiry.