One embodiment of the present invention is a unique fuel cell system. Another embodiment is a unique desulfurization system. Yet another embodiment is a method of operating a fuel cell system. Other embodiments include apparatuses, systems, devices, hardware, methods, and combinations for fuel cell systems and desulfurization systems. Further embodiments, forms, features, aspects, benefits, and advantages of the present application will become apparent from the description and figures provided herewith.