Portable light field cameras have demonstrated capabilities beyond conventional cameras. In a single snapshot, they enable digital image refocusing, i.e., the ability to change the camera focus after taking the snapshot, and 3D reconstruction. We show that they also achieve a larger depth of field than conventional cameras while maintaining the ability to reconstruct detail at high resolution. More interestingly, we show that their depth of field is essentially inverted compared to regular cameras. Crucial to the success of the light field camera is the way it samples the light field, trading off spatial vs. angular resolution, and how aliasing affects the light field. We present a novel algorithm that estimates a full resolution sharp image and a full resolution depth map from a single input light field image. The algorithm is formulated in a variational framework and it is based on novel image priors designed for light field images. We demonstrate the algorithm on synthetic and real images captured with our own light field camera, and show that it can outperform other computational camera systems.