Bismuth oxide based electrolytes are well known for their high oxide ion conductivity at intermediate temperatures (300-700C). Indeed, the defect fluorite structured -phase of Bi2O3 shows the highest known oxide ion conductivity of any material. Unfortunately this phase is only stable above 730C and much research has been carried out on stabilising this phase to lower temperatures through solid solution formation with other oxides. The work described in this thesis examines the structure-conductivity relationships in several substituted bismuth oxide systems. The effects of Nb5+, Y3+ and Pb2+ substitutions for Bi3+ have been examined using a combination of neutron and X-ray diffraction. Conductivity measurements have been performed on selected compounds using a. c. impedance spectroscopy. Nb5+ substituted systems show extensive superlattice ordering of the fluorite subcell. Three structural types have been examined in the Bi2O3-Nb2O5 binary oxide system, the Type II (incommensurately modulated) structure, the Type III (commensurately modulated) tetragonal structure and the Type IV (Aurivillius) layered structure. The relationship between these structures and that of fluorite is discussed. A detailed investigation of the highly conducting phase -Bi3YO6 was carried out using total neutron scattering methods. The average structure shows oxide ions disordered on the crystallographic scale and distributed over 3 crystallographic sites in the Fm-3m cubic cell. Evidence from the total neutron scattering analysis reveals further detail on local ordering and has provided the first physical evidence of <110> vacancy ordering in a substituted bismuth oxide based fluorite. Double substitution in Bi2O3 has been examined in the systems Bi2O3-Nb2O5-Y2O3 and Bi2O3-PbO-Y2O3. In the Pb2+/Y3+ substituted system, three temperature regions were evident in the Arrhenius plots of total conductivity and were reflected in the thermal expansion of the cubic lattice parameter. The difference between these regions is less pronounced in the Bi2O3-Nb2O5-Y2O3 system with essentially two linear regions identified and an intermediate temperature region. Subtle redistributions of oxide ions are believed to be associated with these transitions. New phases have been examined in the Bi2O3-PbO system and initial structural characterisation of the high temperature phases at compositions Bi3PbO5.5 and Bi4PbO7 has been carried out.