A solid oxide fuel cell (SOFC) is a solid-state energy conversion system that converts chemical energy into electrical energy and heat at elevated temperatures. Its bipolar cells are electrochemical devices with an anode,electrolyte, and cathode that can be arranged in a planar or tubular design with separated gas chambers for fuel and oxidant. Single chamber setups have bipolar cells with reaction selective electrodes and no separation between anode and cathode compartments. A nickel/yttria-stabilized-zirconia (YSZ) cermet is the most investigated and currently most widespread anode material for the use with hydrogen as fuel. In recent years, however, doped ceria cermet anodes with nickel or copper and ceria as the ceramic phase have been introduced together with ceria as electrolyte material for the use with hydrocarbon fuels. The state-of-the-art electrolyte material is YSZ of high ionic and nearly no electronic conductivity at temperatures between 800-1000 °C. In order to reduce SOFC system costs, a reduction of operation temperatures to 600-800 °C is desirable and electrolytes with higher ionic conductivities than YSZ are aimed for such as bismuth oxide, lanthanum gallate or mixed conducting ceria and the use of thin electrolytes. Proton conducting perovskites are researched as alternatives to conventional oxygen conducting electrolyte materials. At the cathode, the reduction of molecular oxygen takes place predominantly on the surface. Today's state-of-the-art cathodes are La x Sr 1 - x MnO 3 - δ for SOFC operating at high temperature i.e. 800-1000 °C, or mixed conducting La x Sr 1 - x Co y Fe 1 - y O 3 - δ for intermediate temperature operation, i.e. 600-800 °C. Among the variety of alternative materials, Sm x Sr 1 - x CoO 3 - δ and Ba x Sr 1 - x Co x Fe 1 - x O 3 - δ are perovskites that show very good oxygen reduction properties. This paper reviews the materials that are used in solid oxide fuel cells and their properties as well as novel materials that are potentially applied in the near future. The possible designs of single bipolar cells are also reviewed.