This paper begins with a brief review of the thermodynamic and electrochemical fundamentals of a solid oxide fuel cell (SOFC). Issues concerning energy budget and ideal energy conversion efficiency of the electrochemical processes in an SOFC are addressed. Chemical equilibrium is then discussed for the situations with internal reforming and shift reactions as an SOFC is fed with hydrocarbon fuel. Formulations accounting for electrical potential drops incurred by activation polarization, ohmic polarization, and concentration polarization are reviewed. This leads to a discussion on numerical modeling and simulation for predicting the terminal voltage and power output of SOFCs. Key features associated with numerical simulation include strong coupling of ion transfer rates, electricity conduction, flow fields of fuel and oxidizer, concentrations of gas species, and temperature distributions. Simulation results based primarily on authors’ research are presented as demonstration. The article concludes with a discussion of technical challenges in SOFCs and potential issues for future research.

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