Some aspects of the theory of generalized quantifiers related to linguistics are considered. Syntactically, generalized polyadic quantifiers appear in expressions \(Qx_ 1...x_ n\cdot \phi (x_ 1,...,x_ n)\); this is interpreted set-theoretically as \(\| \phi \| \in Q\). The main goal of the paper is to discuss the role of polyadic quantification and to compare it with more traditional unary quantification. Some linguistic examples of polyadic quantifiers are given. Then some classes of quantifiers are introduced, such as logical (invariant under permutations of individuals), oriented, scopeless, monotone quantifiers etc. Special attention is payed to ``Fregean'' quantifiers which can be reduced to iterations of unary quantifiers. A lot of recent (and some new) results connecting different types of quantifiers are presented. For example, on a finite domain a binary quantifier is definable by a Boolean combination of iterations of logical unary quantifiers iff it is logical and right-oriented.