Big data applications routinely involve diverse datasets: relations at or nested, complex-structure graphs, documents, poorly struc-tured logs, or even text data. To handle the data, application designers usually rely on several data stores used side-by-side, each capable of handling one or a few data models, and each very ee-cient for some, but not all, kinds of processing on the data. A current limitation is that applications are written taking into account which part of the data is stored in which store and how. This fails to take advantage of (i) possible redundancy, when the same data may be accessible (with diierent performance) from distinct data stores; (ii) partial query results (in the style of materialized views) which may be available in the stores. We present ESTOCADA, a novel approach connecting applications to the potentially heterogeneous systems where their input data resides. ESTOCADA can be used in a polystore setting to transparently enable each query to beneet from the best combination of stored data and available processing capabilities. ESTOCADA leverages recent advances in the area of view-based query rewriting under constraints, which we use to describe the various data models and stored data. Our experiments illustrate the signiicant performance gains achieved by ESTOCADA.