In this paper, we present a learning based approach to depth fusion, i.e., dense 3D reconstruction from multiple depth images. The most common approach to depth fusion is based on averaging truncated signed distance functions, which was originally proposed by Curless and Levoy in 1996. While this method achieves great results, it can not reconstruct surfaces occluded in the input views and requires a large number frames to filter out sensor noise and outliers. Motivated by large 3D model databases and recent advances in deep learning, we present a novel 3D convolutional network architecture that learns to predict an implicit surface representation from the input depth maps. Our learning based fusion approach significantly outperforms the traditional volumetric fusion approach in terms of noise reduction and outlier suppression. By learning the structure of real world 3D objects and scenes, our approach is further able to reconstruct occluded regions and to fill gaps in the reconstruction. We evaluate our approach extensively on both synthetic and real-world datasets for volumetric fusion. Further, we apply our approach to the problem of 3D shape completion from a single view where our approach achieves state-of-the-art results.