Three cobalt-based oxides operating at the Co(III)/Co(II) redox couple have been investigated as potential cathode materials for the intermediate-temperature solid oxide fuel cells (IT-SOFCs). X-ray absorption spectroscopy measurements confirmed that both the oxygen-deficient perovskite Sr[subscript 0.7]Y[subscript 0.3]CoO[subscript 2.65-delta] (SYCO) and the double-perovskite Ba₂[Co][Bi[subscript x]Sc[subscript 0.2]Co[subscript 1.8-x]][subscript O6-delta] (x = 0.1 and 0.2) (BBSC) contain high-spin Co(III) in the bulk at room temperature and thus avoid the thermally driven spin-state crossover of the Co(III) ions usually observed in other cobalt-containing perovskite oxides. Electrochemical characterizations demonstrated that both cobalt oxides operating on the Co(III)/Co(II) redox couple are equally catalytically active for the oxygen reduction reaction as those operating on the Co(IV)/Co(III) redox couple. With an LSGM electrolyte-supported single test cell and NiO+GDC as anode, the maximum power densities Pmax at 800 ºC reach 927 and 1180 mW·cm⁻² for SYCO and BBSC cathodes, respectively. The oxygen-deficient perovskites Sr[subscript 1-x]R[subscript x]CoO[subscript 3-delta] (R = Eu-Ho, Y, x [approximately equal] 0.3) are identified as a new class of cathode materials for IT-SOFCs in this dissertation. On the other hand, the layered Ba2Co9O14 (BCO) containing the low-spin Co(III) at room temperature undergoes a thermally driven spin-state crossover, which has prevented it from being evaluated as the cathode of IT-SOFCs. This problem was overcome by fabrication of a 50-50 wt.% BCO + SDC (Sm[subscript 0.2]Ce[subscript 0.8]O[subscript 1.9]) composite cathode. The addition of SDC not only improved the adhesion to the electrolyte, but also enhanced the electrocatalytic activity for the oxygen reduction reaction. The composite cathode delivers a nearly stable P[subscript max] of ~450 mW·cm-2 at 800 °C in an LSGM electrolyte-supported single test cell. In addition, the electrochemical lithium intercalation process in the monoclinic Nb12O29 was studied with a Li/Nb₁₂O₂₉ half-cell, and the results showed that it can reversibly incorporate a relatively large amount of Li-ions in the voltage window of 2.5-1.0 V at a slow discharge/charge rate while retaining structural integrity. Compared with that of the bare Nb₁₂O₂₉, samples with carbon coating show an improved rate capability. The lithium insertion mechanism into Nb₁₂O₂₉ has also been discussed in terms of sites available to the lithium ions / text