What can hierarchies do for data warehouses? H. V. Jagadish, Laks V. S. Lakshmanan and Divesh Srivastava. Data in a warehouse typically has multiple dimensions of interest, such as location, time, and product. It is well-recognized that these dimensions have hierarchies defined on them, such as ``store-city-state-region'' for location. The standard way to model such data is with a star/snowflake schema. However, current approaches do not give a first-class status to dimensions. Consequently, a substantial class of interesting queries involving dimension hierarchies and their interaction with the fact tables are quite verbose to write, hard to read, and difficult to optimize. We propose the SQL(H) model and a natural extension to the SQL query language, that gives a first-class status to dimensions, and we pin down its semantics. Our model permits structural and schematic heterogeneity in dimension hierarchies, situations often arising in practice that cannot be modeled satisfactorily using the star/snowflake approach. We show using examples that sophisticated queries involving dimension hierarchies and their interplay with aggregation can be expressed concisely in SQL(H). By comparison, expressing such queries in SQL would involve a union of numerous complex sequences of joins. Finally, we develop an efficient implementation strategy for computing SQL(H) queries, based on an algorithm for hierarchical joins, and the use of dimension indexes.