The high oxide ion conductivity of solid solutions of bismuth oxide was initially discovered by Takahashi and coworkers. The bismuth oxide based compounds are much better solid electrolytes than the well-known stabilized zirconia. The only difficulty which has prevented their use in high temperature fuel cells and gas sensors up to now is their instability against reduction at low oxygen partial pressures. In this article, we review the structural properties, thermal expansion, electrical conductivity, thermodynamic stability, and surface properties of bismuth oxide and solid solutions of bismuth oxide with face centred cubic, rhombohedral, tetragonal or layer structures.