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 computational issues that arise in its interpretation.