Proton-pumping NADH:ubiquinone oxidoreductase (complex I) is the largest and most complicated enzyme of the respiratory chain. Fourteen central subunits represent the minimal form of complex I and can be assigned to functional modules for NADH oxidation, ubiquinone reduction, and proton pumping. In addition, the mitochondrial enzyme comprises some 30 accessory subunits surrounding the central subunits that are not directly associated with energy conservation. Complex I is known to release deleterious oxygen radicals (ROS) and its dysfunction has been linked to a number of hereditary and degenerative diseases. We here review recent progress in structure determination, and in understanding the role of accessory subunits and functional analysis of mitochondrial complex I. For the central subunits, structures provide insight into the arrangement of functional modules including the substrate binding sites, redox-centers and putative proton channels and pump sites. Only for two of the accessory subunits, detailed structures are available. Nevertheless, many of them could be localized in the overall structure of complex I, but most of these assignments have to be considered tentative. Strikingly, redox reactions and proton pumping machinery are spatially completely separated and the site of reduction for the hydrophobic substrate ubiquinone is found deeply buried in the hydrophilic domain of the complex. The X-ray structure of complex I from Yarrowia lipolytica provides clues supporting the previously proposed two-state stabilization change mechanism, in which ubiquinone redox chemistry induces conformational states and thereby drives proton pumping. The same structural rearrangements may explain the active/deactive transition of complex I implying an integrated mechanistic model for energy conversion and regulation. This article is part of a Special Issue entitled Respiratory complex I, edited by Volker Zickermann and Ulrich Brandt.