A characterization of the expressive power of synchronous tree-adjoining grammars (STAGs) in terms of tree transducers (or equivalently, synchronous tree substitution grammars) is developed. Essentially, a STAG corresponds to an extended tree transducer that uses explicit substitution in both the input and output. This characterization allows the easy integration of STAG into toolkits for extended tree transducers. Moreover, the applicability of the characterization to several representational and algorithmic problems is demonstrated.