Bi-rich ternary oxides of the system Bi2O3-Re2O7 with composition Bi2-xRexO3+2x have crystal structures with fluorite-like subunit cells. Several superunit cells are detected for different Re contents by X-ray and electron diffraction : Materials around x = 0.05 are characterized by a root 2 x root 2 x 1 tetragonal supenrnit cell of the P-Bi,O, type. For higher Re contents a beta-->delta phase transition takes place. Around x = 0.1 a 3 x 3 x 3 tetragonal superunit cell develops, whereas for x = 0.2, a rhombohedral distortion is present. According to the vibrational spectroscopic investigations, the Re guest ion enters the lattice as ReO4 tetrahedra as well as with six-fold oxygen coordination. By diffuse reflectance spectroscopy it is shown that Re doping influences the band structure via the introduction of impurity levels within the band gap. Thus, the system Bi2O3-Re2O7 is suitable for fine-tuning the band gap between approximate to 2.2 and 3.0 eV.