This chapter describes the concept, electrochemical reactions, and fabrication of a solid oxide fuel cell (SOFC). The chapter initially describes how SOFC systems differ from other electrical devices and how they differ from other types of fuel cells; for example, they are all solid state (ceramics), run at high temperature and have the potential for directly running off hydrocarbon fuels. The chapter then studies the basic principles of the fuel cell, and describes each of the components in more detail (the anode, cathode, and electrolyte). The discussion then moves on to how single SOFC’s can be stacked in a number of ways, to form systems, and what the advantages and disadvantages of each is. Finally, the chapter discusses one such SOFC system in more detail, that of the microtubular SOFC. Here the chapter examines how these microtubes are made, what they are made from, and how they have the potential for running at low temperature for small applications such as auxiliary power units (APU), for example. The paper then concludes with some micro and macro-modeling on the microtubular SOFC, describing issues such as mass and thermal transport, the effect of altering a number of parameters, and how the modeling results compare to real data. The chapter concludes with some future directions on solid oxide fuel cells.