Graphical abstract A review on the mathematical models for gas transport in micro/nano-porous electrodes of solid oxide fuels is presented. Based on the Knudsen number and complexity of fuel gas systems, the different gas diffusion models show different advantages/disadvantages. The review then focuses on the different techniques of gas diffusivity measurements in solid oxide fuel cells. Such direct gas diffusivity measurement techniques largely facilitate the efficient pre-evaluation of energy loss in solid oxide fuel cells. Such pre-evaluation improves our understanding on the parameters associated with the electrode microstructure of solid oxide fuel cells, such as porosity, thickness, and tortuosity. Highlights ► Reviews models for gas transport in electrodes of solid oxide fuel cells (SOFCs). ► Discusses recently-developed devices for direct diffusivity measurement in SOFCs. ► Shows that diffusivity measurement facilitates the research on SOFC electrodes.