This paper summarizes the governing equations and multi-scale modeling methods for the thermal, electrical and mass transports, reformation, catalytic and sulfurization reactions in SOFCs. SOFCs have the advantage of fuel flexibility by converting a broad range of fuels such as hydrogen, carbon monoxide, methane and other hydrocarbons into electricity, but require in depth understanding of the processes of reformation, catalysis， coke and vulcanization. The transports of fuel and oxidant, heat and electricity, chemical and electrochemical reactions may be described by solving their coupled partial differential equations. The multiscale model based on these equations and the material microstructures are used to study the effects of operating conditions, material properties and geometrical configurations on the SOFC performance. Quantitative analysis and design optimization of the material compositions and the stack configurations are helpful for accelerating the development of SOFC technology.