Polarization, or the path traced by the electric field vector, is a fundamental characteristic of electromagnetic radiation, of crucial importance in both science and technology. Unique optical elements known as metasurfaces allow polarization to be modified at-will, point-by-point across a plane. In this thesis, we explore these metasurface polarization optics. In particular, we develop several theoretical approaches to designing them, including an approach we dub Jones matrix Fourier optics which generalizes and extends previous work in this area. We apply this to realize a variety of technologically interesting optical devices, from polarization-sensitive holograms to polarimeters and a compact camera to record polarization state over a photographic scene, of potential interest in remote sensing applications.