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Query containment is the problem of checking whether for all databases the answer to a query is a subset of the answer to a second query. In several data management tasks, such as data integration, mobile computing, etc., the data of interest are only accessible through a given set of views. In this case, containment of queries should be determined relative to the set of views, as already noted in the literature. Such a form of containment, which we call view-based query containment, is the subject of this paper. The problem comes in various forms, depending on whether each of the two queries is expressed over the base alphabet or the alphabet of the view names. We present a thorough analysis of view-based query containment, by discussing all possible combinations from a semantic point of view, and by showing their mutual relationships. In particular, for the two settings of conjunctive queries and two-way regular path queries, we provide both techniques and complexity bounds for the different variants of the problem. Finally, we study the relationship between view-based query containment and view-based query rewriting.