A and " 1 " 1 " 4B surfaces were prepared by molecular-beam epitaxy (MBE) and analyzed in situ by photoelectron spectroscopy of the Ga and As 3d core levels using synchrotron radiation. An overview of the results is given. For each surface also a brief summary of its structure is added. It is shown how surface corelevel shifts (SCLS) act as a tool supporting the structure evaluation of these surfaces. The (001) and (110) surfaces are touched only briefly for comparison. The (111) surfaces are discussed more deeply. The high-index surfaces can be characterized as follows: (113)A exhibits a low-energy surface and a new type of reconstruction which consists of As-dimer zig-zag chains; (112)A and " 1 " 1 " 2B are heavily faceted and (114)A and " 1 " 1 " 4B are quite well understood in analogy to the (001) surface.Recently, high-index III±V semiconductor surfaces achieved great interest as possible substrates for the growth of low-dimensional quantum structures. The nonpolar {112} Review Article