Oxygen transport (including oxygen mobility and surface reactivity) is one of the important factors governing electrochemical activity of solid oxide fuel cells electrodes as well as oxygen and hydrogen separation membranes based on materials with mixed oxide-ionic and electronic conductivity. In this work, oxygen mobility data obtained for a series of materials destined for such devices using modern techniques of oxygen isotope heteroexchange are summarized. Series of solid oxide fuel cells’ and membranes’ materials were studied by isotope exchange of their oxygen with 18O2 and C18O2 in isothermal and temperature-programmed modes using closed and flow reactors and data analysis based on developed model of oxygen diffusion and exchange. For solid electrolytes’ materials (Sc- and Ce-doped zirconia) as well as for proton-conducting materials [Ln5.5(Mo,W)O11.25], the effect of composition heterogeneity on the oxygen mobility was demonstrated. For Ln6 – xWO12 – δ, a strong effect of structure on the oxygen mobility was demonstrated. For oxides with asymmetric structure, where oxygen migration proceeds via cooperative mechanisms [La2(Mo,W)2O9, (Ln,Ca)2NiO4], the doping hampers the cooperative migration, resulting in oxygen mobility deterioration and sometimes forming additional slow diffusion channels. In the PrNi0.5Co0.5O3–Ce0.9Y0.1O2 nanocomposites that are materials of the solid oxide fuel cells’ cathode and functional layer of the oxygen separation membranes, two diffusion channels were observed, where more mobile oxygen corresponds to the fluorite phase and interfaces; less mobile, to the perovskite phase. This is due to special features of cations redistribution between the phases.