We present a review on fuel cells with emphasis on solid oxide fuel cells (SOFCs). We give an overview of proton exchange membrane, alkaline, phosphoric acid, molten carbonate and direct methanol fuels cells. For SOFCs we discuss electrolytes, anodes, cathodes, interconnects, fabricating processes, materials alternatives and industry. We also give an overview on thermodynamics, electrochemistry and kinetics of fuel cell reactions, mathematical models, fluid dynamics and simulation/computational methods in fuel cells (MM, HF, SE, HF, QM/MM, DFT, MC, MD, FF, Periodic, hybrid, coarse grain). Which are the best SOFCs electrolytes and how they work. We discuss breakthroughs, recent developments and the next generation fuel cells.