Doped barium cerate perovskites, first investigated by Iwahara and co-workers, have ionic conductivities of the order of 20 mS/cm at 800 degrees C making them attractive as fuel cell electrolytes for this temperature region. They have been used to construct laboratory scale fuel cells, which, in addition to performance data, have provided an unexpected insight into the transport processes operating in these materials. In the temperature range of 600-1000 degrees C, the dominant transport process varies from protonic to oxide-ion dominated. This transition has been confirmed by measurement of water vapour transfer in a cell in which the perovskite is exposed to wet hydrogen on both sides. The evolution of transport properties with temperature is discussed in relation to structure. Neutron diffraction studies of doped and undoped barium cerate are reported, revealing a series of phase transitions between ambient temperature and 1000 degrees C. The available literature on chemical stability of cerate perovskites to reduction and attack by carbon dioxide is reviewed in brief.