We report diffraction experiments on some representative Fast Ion Conductors. The structures of anhydrous stoichiometric deuterium (DAl₁₁O₁₇) and silver (AgAl ₁₁O₁₇) beta aluminas have each been determined at four temperatures in the range 4 . 2K - 773K using powder neutron diffraction (PND) data. In DAl₁₁O₁₇, a strong D-O(5) hydroxyl linkage is maintained at all four temperatures .For AgAl₁₁O₁₇ at 4.2K,we have observed, for the first time in metal beta aluminas, a completely ordered cation distribution. The material, which was prepared by a new route, is accurately stoichiometric. At 298K,the silver atoms have become somewhat delocalised and by 773K they are organised in a highly diffuse manner. Single crystal neutron diffraction was used to elucidate the proton distributions in ammonium beta alumina, (NH₄) _1.25Al₁₁- 0_17.125, and the two derivatives (NH₄) _0.78H_0.25Al₁₁0₁₇ and 'HA1₁₁- 0₁₇.In the parent compound, the positions and orientations of the two independant (NH⁺₄) species are such that all protons are involved in favourable hydrogen-bonding schemes. In formation of the first derivative, one of these sites becomes completely depopulated. Our results clarify the thermal behaviour of (NH₄) _1.25Al₁₁0_17.125 and we propose schemes by which stoichiometric beta aluminas are formed from this precursor and the related (H₃0)_1+x- Al₁₁0_17.+x/2. The crystal structures of I-Ag₃PO₄(25°C and 375°C) , II-Ag₃PO₄(650°C) ,II-Na₃PO₄ (γ) (400°C) and the solid solutions Na_3(1-x)Al_xPO₄are described. The high-temperature forms are considered in relation to the fluorite structure and mechanisms for the ionic conduction of these phases are proposed. A single crystal X-ray diffraction study of β-Ag₂SO₄ (25°C) reveals that it is isostructural with thenardite, V-Na ₂SO₄.The high-temperature modifications a-Ag₂SO₄ (490°C) and α-K₂SO₄ (620°C) have been characterised using PND data. A PND experiment on silver (I) fluoride confirms that it adopts the rocksalt structure and we find no firm evidence for a significant population of defects.