This thesis deals with control of fuel cells, focusing on high-temperature protonexchange-membrane fuel cells. Fuel cells are devices that convert the chemical energy of hydrogen, methanol or other chemical compounds directly into electricity, without combustion or thermal cycles. They are efficient, scalable and silent devices that can provide power to a wide variety of utilities, from portable electronics to vehicles, to nation-wide electric grids. Whereas studies about the design of fuel cell systems and the electrochemical properties of their components abound in the open literature, there has been only a minor interest, albeit growing, in dynamics and control of fuel cells. In the relatively small body of available literature, there are some apparently contradictory statements: sometimes the slow dynamics of fuel cells is claimed to present a control problem, whereas in other articles fuel cells are claimed to be easy to control and able to follow references that change very rapidly. These contradictions are mainly caused by differences in the sets of phenomena and dynamics that the authors decided to investigate, and also by how they formulated the control problem. For instance, there is little doubt that the temperature dynamics of a fuel cell can be slow, but users are not concerned with the cell’s temperature: power output is a much more important measure of performance. Fuel cells are very multidisciplinary systems, where electrical engineering, electrochemistry, chemical engineering and materials science are all involved at various levels; it is therefore unsurprising that few researchers can master all of these branches, and that most of them will neglect or misinterpret phenomena they are unfamiliar with.