We present a soft shadow technique for dynamic scenes with moving objects under the combined illumination of moving local light sources and dynamic environment maps. The main idea of our technique is to precompute for each scene entity a shadow field that describes the shadowing effects of the entity at points around it. The shadow field for a light source, called a source radiance field (SRF), records radiance from an illuminant as cube maps at sampled points in its surrounding space. For an occluder, an object occlusion field (OOF) conversely represents in a similar manner the occlusion of radiance by an object. A fundamental difference between shadow fields and previous shadow computation concepts is that shadow fields can be precomputed independent of scene configuration. This is critical for dynamic scenes because, at any given instant, the shadow information at any receiver point can be rapidly computed as a simple combination of SRFs and OOFs according to the current scene configuration. Applications that particularly benefit from this technique include large dynamic scenes in which many instances of an entity can share a single shadow field. Our technique enables low-frequency shadowing effects in dynamic scenes in real-time and all-frequency shadows at interactive rates.