A schema mapping is a specification that describes how data from a source schema is to be mapped to a target schema. Once the data has been transferred from the source to the target, a natural question is whether one can undo the process and recover the initial data, or at least part of it. In fact, it would be desirable to find a reverse schema mapping from target to source that specifies how to bring the exchanged data back. In this paper, we introduce the notion of a recovery of a schema mapping: it is a reverse mapping M for a mapping M that recovers sound data with respect to M. We further introduce an order relation on recoveries. This allows us to choose mappings that recover the maximum amount of sound information. We call such mappings maximum recoveries. We study maximum recoveries in detail, providing a necessary and sufficient condition for their existence. In particular, we prove that maximum recoveries exist for the class of mappings specified by FO-TO-CQ source-to-targe...