While the As-rich 2 × 4 reconstruction of GaAs(001) is well explained by the so-called β2 structure, the atomic structure of the Ga-rich 4 × 2 phase has been discussed for a long time. In this review, the most important structural models for the GaAs(001) (4 × 2)/c(8 × 2) surface are compared from different theoretical and experimental points of view. The selected reconstructions include the recently proposed ζ model, a new mixed dimer model, and the well-known β, β2, Cerdà and Skala models. The different structures are compared on the basis of total energy calculations, simulations of STM experimental images and interpretation of X-ray diffraction data. Only the ζ model satisfies all criteria, and provides therefore a satisfactory explanation of the atomic structure of GaAs(001)-(4 × 2).