This article presents a brief review on modeling philosophies of solid-oxide fuel cells (SOFCs) including an introduction to SOFC components and their functions. While a plethora of numerical models is available for SOFC modeling and simulation, this paper focuses on a general overview on mathematical model equations that represent the physico-chemical processes occurring in SOFCs and their boundary conditions. Electrochemical model equations, their simplifications, significance, and solution methods are discussed. Charge transfer chemistry is described in detail from a global as well as from elementary charge transfer perspective. Principles of heterogeneous reforming chemistry on conventional nickel cermet anodes, evaluation of rate expressions, and the implementation of the thermo chemistry into SOFC flow models are described. Results of numerical simulations are presented for configurations ranging from complex stacks to simple zero dimensional electrochemical systems. © by Oldenbourg Wissenschaftsverlag.