A core problem that must be solved by any practical visual SLAM system is the need to obtain correspondences throughout the image stream captured by a moving camera. Correspondences enable joint estimation of a moving camera's trajectory together with a 3D map of the observed scene. Visual SLAM pipelines commonly obtain correspondence through sparse feature matching techniques and construct maps using a composition of point, line or other simple primitives. The resulting sparse feature map representations provide sparsely furnished, incomplete reconstructions of the observed scene. Related techniques from multiple view stereo (MVS) achieve high quality dense reconstruction by obtaining dense correspondences over calibrated image sequences. Despite the usefulness of the resulting dense models, these techniques have been of limited use in visual SLAM systems. The computational complexity of estimating dense surface geometry has been a practical barrier to its use in real-time SLAM. Furthermore, MVS algorithms have typically required a fixed length, calibrated image sequence to be available throughout the optimisation --- a condition fundamentally at odds with the online nature of SLAM. With the availability of massively-parallel commodity computing hardware, we demonstrate new algorithms that achieve high quality incremental dense reconstruction within online visual SLAM. The result is a live dense reconstruction (LDR) of scenes that makes possible numerous applications that can utilise online surface modelling, for instance: planning robot interactions with unknown objects, augmented reality with characters that interact with the scene, or providing enhanced data for object recognition. The core of this thesis goes beyond LDR to demonstrate fully dense visual SLAM. We replace the sparse feature map representation with an incrementally updated, non-parametric, dense surface model. By enabling real-time dense depth map estimation through novel short baseline MVS, we can continuously update the scene model and further leverage its predictive capabilities to achieve robust camera pose estimation with direct whole image alignment. We demonstrate the capabilities of dense visual SLAM using a single moving passive camera, and also when real-time surface measurements are provided by a commodity depth camera. The results demonstrate state-of-the-art, pick-up-and-play 3D reconstruction and camera tracking systems useful in many real world scenarios.