In this talk we will address the problem of 3D reconstruction of rigid and deformable objects from a single depth video stream. Traditional 3D registration techniques, such as ICP and its variants, are wide-spread and effective, but sensitive to initialization and noise due to the underlying correspondence estimation procedure. Therefore, we have developed SDF-2-SDF, a dense, correspondence-free method which aligns a pair of implicit representations of scene geometry, e.g. signed distance fields, by minimizing their direct voxel-wise difference. In its rigid variant, we apply it for static object reconstruction via real-time frame-to-frame camera tracking and posterior multiview pose optimization, achieving higher accuracy and a wider convergence basin than ICP variants. Its extension to scene reconstruction, SDF-TAR, carries out the implicit-to-implicit registration over several limited-extent volumes anchored in the scene and runs simultaneous GPU tracking and CPU refinement, with a lower memory footprint than other SLAM systems. Finally, to handle non-rigidly moving objects, we incorporate the SDF-2-SDF energy in a variational framework, regularized by a damped approximately Killing vector field. The resulting system, KillingFusion, is able to reconstruct objects undergoing topological changes and fast inter-frame motion in near-real time.