A novel framework for joint monocular 3D tracking and reconstruction is described that can handle untextured objects, occlusions, motion blur, changing background and imperfect lighting, and that can run at frame rate on a mobile phone. The method runs in parallel (i) level set based pose estimation and (ii) continuous max flow based shape optimisation. By avoiding a global computation of distance transforms typically used in level set methods, tracking rates here exceed 100Hz and 20Hz on a desktop and mobile phone, respectively, without needing a GPU. Tracking ambiguities are reduced by augmenting orientation information from the phone's inertial sensor. Reconstruction involves probabilistic integration of the 2D image statistics from keyframes into a 3D volume. Per-voxel posteriors are used instead of the standard likelihoods, giving increased accuracy and robustness. Shape coherency and compactness is then imposed using a total variational approach solved using globally optimal continuous max flow.