Acceptor-doped oxide ceramics such as Zn-doped BaTiO3 show a slow, reversible conductivity enhancement by 1-3 orders of magnitude at high temperature, > ~ 400oC, on application of a small dc bias [1]. With Ca-doped BiFeO3, a similar but much more dramatic effect, with a conductivity enhancement of 4-5 orders of magnitude, occurs rapidly at room temperature and is reversible with some hysteresis on removing the bias [2]. Donor-doped materials such as oxygen-deficient rutile, TiO2, show the opposite effect of a decrease in conductivity with a small dc bias [3].The conductivity enhancement in Ca-doped BiFeO3 is not associated with Schottky barrier effects at the sample-electrode interfaces and is not filamentary. It is instead associated with the sample bulk, i.e. grains and grain boundaries, and in the case of BiFeO3, it is isotropic. The conductivity changes are voltage-dependent and are observed with samples that are 1-2 mm thick and applied voltages as small as 2 V. The effect that we observe in BiFeO3 is not a 'traditional' memristive effect as it is reversible on removing the dc bias and does not require an initial electroforming stage. Possible implications of this effect for the dielectric breakdown of dielectrics will be discussed. A mechanism for conductivity enhancement in acceptor-doped oxides has been proposed that involves p-type conduction associated with creation and location of holes on underbonded oxide ions [1-3]. By contrast, the proposed mechanism for conductivity decrease in donor-doped rutile involves the trapping of mobile carriers at sample surfaces. In both sets of cases, there is clear evidence that at sample surfaces, reaction with oxygen in the atmosphere can have a similar effect, but smaller in magnitude, to the effect of dc bias. There is increasing evidence in a diverse range of materials and investigations that under certain conditions, oxygen may be redox-active, especially at sample surfaces, as shown by the presence of peroxide and superoxide species in which oxygen has an intermediate oxidation state. We have recently found [4] that oxide ion conducting, yttria-stabilised zirconia, YSZ, shows increasing p-type conductivity on application of a small bias at high temperatures, which is attributed to redox activity of underbonded oxide ions; under these conditions, YSZ becomes a mixed conductor, which may lead to undesirable consequences for the use of YSZ ceramics as the electrolyte in solid oxide fuel cells. There is much current interest in ‘anomalous capacities’ of certain lithium battery cathode materials, which is also attributed to redox activity of oxygen, in addition to the usual, redox-active transition metal components. An overview of these recent developments in electroceramic materials will be given.