We present a novel approach for real-time joint reconstruction of 3D scene motion and geometry from binocular stereo videos. Our approach is based on a novel variational halfway-domain scene flow formulation, which allows us to obtain highly accurate spatiotemporal reconstructions of shape and motion. We solve the underlying optimization problem at real-time frame rates using a novel data-parallel robust non-linear optimization strategy. Fast convergence and large displacement flows are achieved by employing a novel hierarchy that stores delta flows between hierarchy levels. High performance is obtained by the introduction of a coarser warp grid that decouples the number of unknowns from the input resolution of the images. We demonstrate our approach in a live setup that is based on two commodity webcams, as well as on publicly available video data. Our extensive experiments and evaluations show that our approach produces high-quality dense reconstructions of 3D geometry and scene flow at real-time frame rates, and compares favorably to the state of the art.