Model transformations are a key element in the OMG's Model Driven Development agenda. They did not begin here: the fundamental idea of transforming, automatically, one model into another is at least as old as the computer, provided that we take a sufficiently broad view of what a model is. In many contexts, people have encountered the need for bidirectional transformations. In this survey paper we discuss the various notions of bidirectional transformation, and their motivation from the needs

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... software engineering. We discuss the state of the art in work targeted specifically at the OMG's MDD initiative, and also, briefly, related work from other communities. We point out some areas which are so far relatively under-researched, and propose research topics for the future.