Metasurfaces, nanophotonic arrays of phase shifting elements with subwavelength spacing, may have elements designed with form birefringence. This makes metasurfaces a particularly interesting platform for new polarization optics. In new work published in Science, we present a unifying mathematical formalism, matrix Fourier optics, that generalizes a large body of past work on this subject and suggests new devices. We use matrix Fourier optics to design diffraction gratings whose orders analyze arbitrarily selected polarization states. We mount such a grating in front of a camera to make an extremely compact, snapshot polarization camera which can be used for practical polarization photography. We show how this metasurface polarization camera can be used in a variety of practical problems, such as imaging stress in transparent plastics and determining surface orientation of specular objects. This camera may have wide-reaching applications in machine vision and remote sensing. This manuscript can be found here. See also a press release and a short video, both produced by Harvard SEAS.