We focus on the research required to establish a foundation for the evolving needs of visualization systems. Three main topics underpin these needs: models, the need for abstractions to describe the core components of the visualization process and the interfaces between them, including users and their behavior; validation, the problem of determining whether visualizations meet consistency and effectiveness criteria on test data or measures; and systems, the design, realization, and operational problems of systems integrating a range of functionalities to give scientists a working environment for visualization. We outline key aspects of each topic, commenting on the current status of work and isolating areas that require significant research. We conclude by suggesting strategies to initiate this research