The unique properties of tree-adjoining grammars (TAG) present a challenge for the application of TAGs beyond the limited confines of syntax, for instance, to the task of semantic interpretation or automatic translation of natural language. We present a variant of TAGs, called synchronous TAGs, which characterize correspondences between languages. The formalism's intended usage is to relate expressions of natural languages to their associated semantics represented in a logical form language, or to their translates in another natural language; in summary, we intend it to allow TAGs to be used beyond their role in syntax proper. We discuss the application of synchronous TAGs to concrete examples, mentioning primarily in passing some comp...