The structural crystallography of the mixed-ion conductor BaCe(1 - x)Ln(x)O(3 - delta) and the parent compound BaCeO3 are reviewed from the perspective of neutron powder diffraction results. High-resolution, time-of-flight, powder diffraction has been used to verify the unit cell metric, and to correct the setting of this metric to the space group for both the undoped phase and for Y- and Nd-doped material. Key superlattice reflections are utilised to disprove the structural phase transitions inferred from Raman spectroscopy in temperature and Nd dopant concentration, with high-resolution powder diffraction showing the correct crystal symmetries in both cases. Crystal structure refinements have shown that negligible perturbation of the parent compound structure occurs on Y- and Nd-doping, and the extrinsic vacancy was found to be ordered on one of the two crystallographically independent oxygen atoms. A possible structural site for the proton has been proposed from measurements made at low temperatures and the potential for more detailed neutron diffraction studies is discussed.