Distributed query processing (DQP) has been widely used in data intensive applications where data of relevance to users are stored at multiple locations. This paper argues: (i) that DQP can be important in the Grid, as a means of providing high-level, declarative languages for integrating data access and analysis; and (ii) that the Grid provides resource management facilities that are useful to developers of DQP systems. As well as discussing and illustrating how DQP technologies can be deployed within the Grid, the paper describes Polar*, a prototype implementation of a DQP system running over Globus. Polar* can handle complex data by adopting the ODMG object model and its query language OQL, which supports the invocation of user-defined operations. The Globus components are accessed through the MPICH-G interface rather than in a lower level way. A case study from bioinformatics is used throughout the paper, to show the benefits of the approach.