Complex I (NADH:ubiquinone oxidoreductase) is the first and largest enzyme in the respiratory chains in mitochondria and bacteria. It is a proton pump that converts redox energy derived from oxidation of food-stuffs into the trans-membrane proton motive force by pumping protons out of mitochondria or from the bacterial cytosol. In humans, it is an assembly of 45 different proteins, making it one of the most complicated enzymes yet described. Its dysfunction is associated with many neurodegenerative diseases, and, since it is a major site of generation of reactive oxygen species, it may be involved in the ageing process also. Both mitochondrial and bacterial complexes I are L-shaped assemblies with a hydrophobic arm embedded in the inner membrane of mitochondria or in the membrane surrounding the bacterial cytosol, and a hydrophilic arm protruding into the mitochondrial matrix or the bacterial cytoplasm. Our research concerns the determination of the high resolution structure of bacterial complex I and understanding how it works. The bacterial enzymes are made of the 14 conserved “core” subunits of the mammalian enzyme, and so they provide a minimal model of the human enzyme. We have determined the structure of the hydrophilic domain of a bacterial complex I by X-ray crystallography, which shows how redox centres link the site where the substrate NADH binds to the enzyme, to the electron acceptor co-enzyme Q, bound in another site more the 100 Å away in the membrane domain of the enzyme. We are working on the structures of the membrane arm and of the intact complex itself with the aim of understanding the proton pumping mechanism.