We present coded focal stack photography as a computational photography paradigm that combines a focal sweep and a coded sensor readout with novel computational algorithms. We demonstrate various applications of coded focal stacks, including photography with programmable non-planar focal surfaces and multiplexed focal stack acquisition. By leveraging sparse coding techniques, coded focal stacks can also be used to recover a full-resolution depth and all-in-focus (AIF) image from a single photograph. Coded focal stack photography is a significant step towards a computational camera architecture that facilitates high-resolution post-capture refocusing, flexible depth of field, and 3D imaging.