Photoelectron diffraction has by now become a versatile and powerful technique for studying surface structures, with special capabilities for resolving chemical and magnetic states of atoms and deriving direct structural information from both forward scattering along bond directions and back-scattering path length differences. Further fitting experiment to theory can lead to structural accuracies in the {plus_minus}0.03 ){Angstrom} range. Holographic inversions of such diffraction data also show considerable promise for deriving local three-dimensional structures around a given emitter with accuracies of {plus_minus}0.2--0.3 {Angstrom}. Resolving the photoelectron spin in some way and using circularly polarized radiation for excitation provide added dimensions for the study of magnetic systems and chiral experimental geometries. Synchrotron radiation with the highest brightness and energy resolution, as well as variable polarization, is crucial to the full exploitation of these techniques
