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The study of generalized quantifiers over the past 15 years has enriched enormously our understanding of natural language determiners (Dets). It has yielded answers to questions raised independently within generative grammar and it has provided us with new semantic generalizations, ones that were basically unformulable without the conceptual and technical apparatus of generalized quantifier theory. Here we overview results of both these types. historical note It was Montague (1969) who first interpreted natural language NPs as generalized quantifiers (though this term was not used by him). But it was only in the early 1980's with the publication of B&C (Barwise and Cooper, 1981) that the study of natural language Dets took on a life of its own. Also from this period are early versions of K&S (Keenan and Stavi, 1986) and Higginbotham and May (1981). The former fed into subsequent formal studies such as van Benthem (1984, 1986) and Westerstähl (1985). The latter focussed on specific linguistic applications of binary quantifiers, a topic initiated in Altham and Tennant (1974), drawing on the mathematical work of Mostowski (1957), and pursued later in a more general linguistic setting in van Benthem (1989) and Keenan (1987b, 1992). Another precursor to the mathematical study of generalized quantifiers is LindstrÅm (1969) who provides the type notation used to classify quantifiers in many later studies. Since these beginnings work on the semantics of Dets has proliferated, both empirically and mathematically. Westerståhl (1989) provides an historical overview up to 1987. Some important collections of articles are: van
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