During the last decade, fuel cells have received enormous attention from research institutions and companies as novel electrical energy conversion systems. In the near future, they will see application in automotive propulsion, distributed power generation, and in low power portable devices (battery replacement). This review gives an introduction into the fundamentals and applications of fuel cells: Firstly, the environmental and social factors promoting fuel cell development are discussed, with an emphasis on the advantages of fuel cells compared to the conventional techniques. Then, the main reactions, which are responsible for the conversion of chemical into electrical energy in fuel cells, are given and the thermodynamic and kinetic fundamentals are stated. The theoretical and real efficiencies of fuel cells are also compared to that of internal combustion engines. Next, the different types of fuel cells and their main components are explained and the related material issues are presented. A section is devoted to fuel generation and storage, which is of paramount importance for the practical aspects of fuel cell use. Finally, attention is given to the integration of the fuel cells into complete systems.