A review is presented of materials that could be utilized as electrolytes (and their associated electrodes and interconnect materials) in solid-state electrolysis cells to convert water (or steam) into hydrogen and oxygen. Electrolytes that function as oxygen ion conductors or proton conductors are considered for various operating temperatures from approximately 80 degrees C to 1000 degrees C. The fundamental electrochemical reactions are reviewed with some discussion of special sources of steam and DC electricity (advanced nuclear) to drive the reactions at the higher temperatures.