Applications that use collections of very large, distributed datasets have become an increasingly important part of science and engineering. With high performance wide-area networks becoming more pervasive, there is interest in making collective use of distributed computational and data resources. Recent work has converged to the notion of the Grid, which attempts to uniformly present a heterogeneous collection of distributed resources. Current Grid research covers many areas from low level infrastructure issues to high level application concerns. However, providing support for efficient exploration and processing of very large scientific datasets stored in distributed archival storage systems remains a challenging research issue. We have initiated an effort that focuses on developing efficient data-intensive applications in a Grid environment. In this paper, we present a framework, called filter-stream programming, that represents the processing units of a data-intensive application as a set of filters, which are designed to be efficient in their use of memory and scratch space. We describe a prototype infrastructure that supports execution of applications using the proposed framework. We present the implementation of two applications using the filter-stream programming framework, and discuss experimental results demonstrating the effects of heterogeneous resources on application performance. (Also cross-referenced as UMIACS-TR-2000-04)