In this paper, the author studies the question of logicality in the context of quantifier languages, in particular, in the context of natural language quantifiers. Given a language, one may ask what it means to say that some constants are ''logical'' and the others ''nonlogical''. The author asks: On what grounds is such a division to be made? This question has been inspired by the fact that currently there exist several alternatives to the standard, i.e., elementary logic; and they play an increasingly important role. The author discusses the question in a model-theoretic framework. In that framework, logicality is something which puts constraints on interpretation. There must be constraints which say, roughly speaking, that interpretation is the same in all models and constraints saying that logical expressions must be ''neutral'' in the sense of not involving any particular individual, property, relation, or state of affairs. The latter kind of constraints is exemplified by a constraint called ''closure under isomorphism''. The author explicates these constraints in the framework of general quantifier languages and studies e.g. some familiar natural language quantifiers, or determiners, from the point of view of his definitions pointing out that certain determiners do not satisfy his criteria of logicality. The paper is a very important approach to the question of logicality since it shows that model theory provides a flexible and natural framework for the question.