Information integration is a key challenge faced by all major organizations, business and governmental ones alike. Two research facets of this challenge that have received considerable attention in recent years are data exchange and data integration. The study of data exchange and data integration has been facilitated by the systematic use of schema mappings, which are high-level specifications that describe the relationship between two database schemas. Schema mappings are typically expressed in declarative languages based on logical formalisms and are chosen with two criteria in mind: (a) expressive power sufficient to specify interesting data interoperability tasks and (b) desirable structural properties, such as query rewritability and existence of universal solutions, that, in turn, imply good algorithmic behavior. Here, we examine these and other fundamental structural properties of schema mappings from a new perspective by asking: How widely applicable are these properties? Which schema mappings possess these properties and which do not? We settle these questions by establishing structural characterizations to the effect that a schema mapping possesses certain structural properties if and only if it can be specified in a particular schema-mapping language. More concretely, we obtain structural characterizations of schema-mapping languages such as globalas-view (GAV) dependencies and local-as-view (LAV) dependencies. These results delineate the tools available in the study of schema mappings and pinpoint the properties of schema mappings that one stands to gain or lose by switching from one schema-mapping language to another. © 2010 ACM.