Generalized quantifier theory (GQ theory, for short) looks like a success story and has become an integral part of most theories of formal semantics. But especially starting with the 1990s many have questioned either its correctness or its relevance. The objections, expressed in the published literature or in professional discussions, are of the form “GQ theory cannot handle …” or “GQ theory has nothing interesting to say about …”, where the dots are filled by names of empirical phenomena or conceptual issues that do not belong among the classical research topics in GQ theory. The present chapter and the next pull together a range of issues that have figured in such objections, and attempt to evaluate what they tell us about GQ theory. To anticipate the conclusions, some of the objections can be rather easily answered by clarifying certain assumptions or by reminding ourselves of assumptions that may have sunk into oblivion. These definitely do not justify a paradigm shift. Other issues, especially those to be introduced in the next chapter, will be seen to have led to a major transformation of how we think about quantification and scope. The role of generalized quantifiers will be reassessed along the way, but they will not disappear from the picture.