This talk will discuss a very general notion of query reformulation: Given a query Q, a set of constraints , a target query language or programming language, and a cost metric, determine if there is an object in the target language that is equivalent to Q relative to the constraints, and if so nd such an object optimizing the cost metric. The problem has a long history in the database community, originally motivated by querying over materialized views. This talk will go over several very recent developments { from a database perspective, but mentioning the relationship to description logics.