Abstract Solid-oxide fuel cells can directly use hydrocarbon or hydrocarbon-derived fuels. Conversion efficiencies can be considerably greater than those of heat engines, with hybrid cycles in combination with heat engines and co-generation promising conversion efficiencies as high as 70%. This paper discusses the fundamental concepts of fuel cells, concentrating on the underlying chemical and electrochemical processes. Fully understanding fuel cell function requires attention to physical and chemical processes that span length scales ranging from atomistic to meter-scale systems. Beyond the electrochemistry that is responsible for electrical energy production, fuel cell function relies on chemically reacting flow, porous-media transport, and heterogeneous thermal chemistry. Especially with hydrocarbon and hydrocarbon-derived fuels, there are interesting scientific and engineering connections, and analogies with combustion science and technology.