Typelogical grammar, in its current incarnations, keeps the general architecture of Lambek's original calculi, but extends this to a more articulate vocabulary of type-forming operations.  Of central importance are the multiplicative operations, used to model grammatical composition; these form the focus of this article. Next to the multiplicatives one can consider additive or Boolean operations and first or second order quantification to handle phenomena of lexical ambiguity, type polymorphism and the management of feature information. Morrill 1994 is a good source of examples for such extensions.