This paper addresses the problem of remapping the disparity range of stereoscopic images and video. Such operations are highly important for a variety of issues arising from the production, live broadcast, and consumption of 3D content. Our work is motivated by the observation that the displayed depth and the resulting 3D viewing experience are dictated by a complex combination of perceptual, technological, and artistic constraints. We first discuss the most important perceptual aspects of stereo vision and their implications for stereoscopic content creation. We then formalize these insights into a set of basic disparity mapping operators. These operators enable us to control and retarget the depth of a stereoscopic scene in a nonlinear and locally adaptive fashion. To implement our operators, we propose a new strategy based on stereoscopic warping of the input video streams. From a sparse set of stereo correspondences, our algorithm computes disparity and image-based saliency estim...