The binary Re1−xMox alloys, known to cover the full range of solid solutions, were successfully synthesized and their crystal structures and physical properties investigated via powder x-ray diffraction, electrical resistivity, magnetic susceptibility, and heat capacity. By varying the Re/Mo ratio, we explore the full Re1−xMox binary phase diagram, in all its four different solid phases: hcp-Mg (P63/mmc), α-Mn (I43m), β-CrFe (P42/mnm), and bcc-W (Im3m), of which the second is non-centrosymmetric with the rest being centrosymmetric. All Re1−xMox alloys are superconductors, whose critical temperatures exhibit a peculiar phase diagram, characterized by three different superconducting regions.