Complex I (NADH:quinone oxidoreductase) is crucial to respiration in many aerobic organisms. In mitochondria, it oxidizes NADH (to regenerate NAD+ for the tricarboxylic acid cycle and fatty-acid oxidation), reduces ubiquinone (the electrons are ultimately used to reduce oxygen to water) and transports protons across the mitochondrial inner membrane (to produce and sustain the protonmotive force that supports ATP synthesis and transport processes). Complex I is also a major contributor to reactive oxygen species production in the cell. Understanding the mechanisms of energy transduction and reactive oxygen species production by complex I is not only a significant intellectual challenge, but also a prerequisite for understanding the roles of complex I in disease, and for the development of effective therapies. One approach to defining a complicated reaction mechanism is to break it down into manageable parts that can be tackled individually, before being recombined and integrated to produce the complete picture. Thus energy transduction by complex I comprises NADH oxidation by a flavin mononucleotide, intramolecular electron transfer from the flavin to bound quinone along a chain of iron-sulfur clusters, quinone reduction and proton translocation. More simply, molecular oxygen is reduced by the flavin, to form the reactive oxygen species superoxide and hydrogen peroxide. The present review summarizes and evaluates experimental data that pertain to the reaction mechanisms of complex I, and describes and discusses contemporary mechanistic hypotheses, proposals and models.