Within the past few years, angle-resolved photoemission from adsorbate core levels has been experimentally investigated in a few laboratories as a new tool for determining surface atomic geometries. This type of measurement is of interest because the initial state is very simple, the emitting site is well defined, and essentially all anisotropy is produced by final-state photoelectron diffraction. Both variable-energy synchrotron radiation up to about 100 eV and standard soft X-ray sources at 1.5 keV have been used for excitation. In studies of various adsorbates (including atomic Na, Se, Te and O, and molecular CO) on transition-metal surfaces (Ni and Cu), several types of anisotropy useful for deriving structural information have been noted. These involve both polar- and azimuthal-angle scans of electron emission direction at constant hv, as well as scans of hv for a fixed normal emission direction. At lower energies, a full multiple-scattering theoretical analysis appears to be necessary, whereas at higher XPS energies, a single-scattering approach has met with some success. Work to date will be briefly reviewed, and the future of the method will be discussed, particularly with reference to the involvement of synchrotron radiation.