The work reported in this thesis is based around substitutions into bismuth oxide, which has proven to be highly adaptable chemically as it can accommodate a wide variety of substituents. The synthesis and characterisation of stabilised δ-Bi₂O₃ related materials containing small amounts of Ca, Ga, Nb and Re are described. A body of work is presented exploring the structural and physical properties of such materials, characterised by neutron powder diffraction, X-ray powder diffraction, electron diffraction, extended X-ray absorption of fine structure measurements, differential thermal analysis and impedance spectroscopy. The structure of two new fluorite-related materials, Bi₆Ca₃ReO₁₅.₅ and Bi₁₀Ca₅ReO₂₃.₅, were studied. Bi₆Ca₃ReO₁₅.₅ formed a face-centred cubic fluorite-related structure and Bi₁₀Ca₅ReO₂₃.₅ a body-centred cubic material that is a 4 x 4 x 4 superstructure of the Bi₆Ca₃ReO₁₅.₅ phase. The structure of novel isostructural materials Bi₂₀Ca₇NbO₃₉.₅ and Bi₁₀.₇₅Ca₄.₃₇₅GaO₂₂ were also investigated. Both materials formed distorted δ-Bi₂O₃ related superstructures, derived as a monoclinic supercell based on a fluorite-related hexagonal subcell. Detailed structural analysis and local environments of cations in the ordered monoclinic fluorite-related superstructure of Bi₉ReO₁₇ are also explored. All materials synthesised in this thesis have structures related to that of δ-Bi₂O₃, which is known to have high oxide ion conducting properties at elevated temperatures. Oxide ion conducting properties are therefore also described.