The Solid Oxide Fuel Cell (SOFC) is an electrochemical device to convert chemical energy of a fuel into electricity at temperatures from about 600 to $1000^{circ}C$. The SOFC offers certain advantages over lower temperature fuel cells, notably its ability to use CO as a fuel rather than being poisoned by it, and high grade exhaust heat for combined heat and power, or combined cycle gas turbine applications. This paper reviews the operating principle, materials for different cell and stack components, cell designs, and applications of SOFCs. Among all designs of Solid Oxide Fuel Cells (SOFCs), the most progress has been achieved with the tubular design. However, the electrical resistance of tubular SOFCs is high, and specific power output $(W/cm^2)$ and volumetric power density $(W/cm^3)$ low. Planar SOFCs, in contrast, are capable of achieving very high power densities.