This paper presents a review of recent publications on mathematical modeling, steady-state and dynamic behavior, and control of polyelectrolyte membrane and solid oxide fuel cells. We limited the scope of this review to these two fuel cell types, which have been studied more, and have been reported to be more promising, than other fuel cell types. Zero-, one-, two-, and three-dimensional models developed to describe the behavior of the fuel cells are reviewed. Essential components of these models are highlighted. Conditions under which a fuel cell exhibits steady state multiplicity are described. Stability of the steady states is discussed. Processes that take place inside the fuel cells and contribute to the existence of multiple time-scales in the fuel cells are examined. Control configurations and strategies proposed and used for the fuel cells are reviewed, and advantages and disadvantages of each are listed. At the end, in view of the current status of the research activities, topics that require fur...