Publisher Summary This chapter discusses the most promising constituents of solid-oxide fuel cells, their advantages and shortcomings, and then the perspectives and the potential to develop advanced materials and better devices. The chapter focuses on the general electrochemical problems. The most important step is searching for sufficiently stable and mechanically strong structures that exhibit promising potential in terms of electrochemistry, such as fluorites, perovskites, pyrochlore,s or brownmillerites, in the case of electrolyte materials. In conventional fuel-cell designs, the electrolyte not only mediates the electrochemical reactions taking place at the anode and cathode, but also separates the fuel from the oxidant to prevent direct combustion.