Over the recent years, we have seen an increasing number of applications in networking, sensor networks, cloud computing, and environmental monitoring, which monitor, plan, control, and make decisions over data streams from multiple sources. We are interested in extending traditional stream processing techniques to meet the new challenges of these applications. Generally, in order to support genuine continuous query optimization and processing over data streams, we need to systematically understand how to address incremental optimization and processing of update streams for a rich class of queries commonly used in the applications. Our general thesis is that efficient incremental processing and re-optimization of update streams can be achieved by various incremental view maintenance techniques if we cast the problems as incremental view maintenance problems over data streams. We focus on two incremental processing of update streams challenges currently not addressed in existing work on stream query processing: incremental processing of transitive closure queries over data streams, and incremental re-optimization of queries. In addition to addressing these specific challenges, we also develop a working prototype system Aspen, which serves as an end-to-end stream processing system that has been deployed as the foundation for a case study of our SmartCIS application. We validate our solutions both analytically and empirically on top of our prototype system Aspen, over a variety of benchmark workloads such as TPC-H and LinearRoad Benchmarks.