Three solid-oxide fuel cell (SOFC) electrolytes, yttria-stabilized zirconia (YSZ), rare-earth–doped ceria (REDC), and lanthanum strontium gallium magnesium oxide (LSGM), are reviewed on their electrical properties, materials compatibility, and mass transport properties in relation to their use in SOFCs. For the fluorite-type oxides (zirconia and ceria), electrical properties and thermodynamic stability are discussed in relation to their valence stability and the size of the host and dopant ions. Materials compatibility with electrodes is examined in terms of physicochemical features and their relationship to the electrochemical reactions. The application of secondary ion mass spectrometry (SIMS) to detect interface reactivity is demonstrated. The usefulness of doped ceria is discussed as an interlayer to prevent chemical reactions at the electrode–electrolyte interfaces and also as an oxide component in Ni–cermet anodes to avoid carbon deposition on nickel surfaces. Finally, the importance of cation diffusivity in LSGM is discussed, with an emphasis on the grain-boundary effects.