Data exchange is the problem where data conforming to a source schema is transformed into data conforming to a target schema. Although the data exchange problem was already described in the 1970s, its logical foundations have not been studied until very recently. A bit over a decade ago data exchange received new significance with the increasing importance of the internet and the various data formats that it has brought with it. Since then, data exchange has become a very active area of database research. In the first place, data exchange of relational data has been investigated. More recently, data exchange research has been extended to other data models such as knowledge bases and XML. The goal of this master's thesis is to summarize the state of the art in data exchange. Therefore, the available literature is surveyed and a selection of the most important results in this area of research is presented. The main issues that will be discussed are finding a proper formalism for expressing expressing the relationship between the source and the target schema, validating the solutions, materializing solutions, and answering queries posed over the target schema with respect to the source data. We focus in the range of this work on data exchange over relational data, knowledge bases and XML data.