The transport of oxygen ions plays a central role in determining the performance or the degradation of perovskite-type oxides in applications as diverse as ceramic capacitors, solid electrolytes, memristive devices and all-oxide electronics. In this Feature Article, experimental data reported in the literature for oxygen diffusion in SrTiO3 and in related titanate, zirconate and cerate perovskite oxides [CaTiO3, BaTiO3, (Na,Bi)TiO3, Pb(Ti,Zr)O-3, CaZrO3, SrZrO3, BaZrO3, SrCeO3, BaCeO3] are reviewed. The two related aims are to draw attention to discrepancies and to identify reliable diffusion data. The physical limit to the diffusivity of oxygen vacancies in a perovskite oxide is also considered.