This paper is concerned with the recovery of temporally coherent estimates of 3D structure and motion of a dynamic scene from a sequence of binocular stereo images. A novel approach is presented based on matching of spatiotemporal quadric elements (stequels) between views, as this primitive encapsulates both spatial and temporal image structure for 3D estimation. Match constraints are developed for bringing stequels into correspondence across binocular views. With correspondence established, temporally coherent disparity estimates are obtained without explicit motion recovery. Further, the matched stequels also will be shown to support direct recovery of scene flow estimates. Extensive algorithmic evaluation with ground truth data incorporated in both local and global correspondence paradigms shows the considerable benefit of using stequels as a matching primitive and its advantages in comparison to alternative methods of enforcing temporal coherence in disparity estimation. Additional experiments document the usefulness of stequel matching for 3D scene flow estimation.