Shadow maps provide a fast and convenient method of identifying shadows in scenes but can introduce aliasing. This paper introduces the Adaptive Shadow Map (ASM) as a solution to this problem. An ASM removes aliasing by resolving pixel size mismatches between the eye view and the light source view. It achieves this goal by storing the light source view (i.e., the shadow map for the light source) as a hierarchical grid structure as opposed to the conventional flat structure. As pixels are transformed from the eye view to the light source view, the ASM is refined to create higher-resolution pieces of the shadow map when needed. This is done by evaluating the contributions of shadow map pixels to the overall image quality. The improvement process is view-driven, progressive, and confined to a user-specifiable memory footprint. We show that ASMs enable dramatic improvements in shadow quality while maintaining interactive rates.