Volume Rendering is an important technique for visualizing three-dimensional scalar data grids and is commonly employed for scientific and medical image data. Direct Volume Rendering (DVR) is a well established and efficient rendering algorithm for volumetric data. Neural rendering uses deep neural networks to solve inverse rendering tasks and applies techniques similar to DVR. However, it has not been demonstrated successfully for the rendering of scientific volume data. In this work, we introduce Deep Direct Volume Rendering (DeepDVR), a generalization of DVR that allows for the integration of deep neural networks into the DVR algorithm. We conceptualize the rendering in a latent color space, thus enabling the use of deep architectures to learn implicit mappings for feature extraction and classification, replacing explicit feature design and hand-crafted transfer functions. Our generalization serves to derive novel volume rendering architectures that can be trained end-to-end directly from examples in image space, obviating the need to manually define and fine-tune multidimensional transfer functions while providing superior classification strength. We further introduce a novel stepsize annealing scheme to accelerate the training of DeepDVR models and validate its effectiveness in a set of experiments. We validate our architectures on two example use cases: (1) learning an optimized rendering from manually adjusted reference images for a single volume and (2) learning advanced visualization concepts like shading and semantic colorization that generalize to unseen volume data. We find that deep volume rendering architectures with explicit modeling of the DVR pipeline effectively enable end-to-end learning of scientific volume rendering tasks from target images.