This review examines two aspects of the structure and function of mitochondrial Complex I (NADH Coenzyme Q oxidoreductase) that have become matter of recent debate. The supramolecular organization of Complex I and its structural relation with the remainder of the respiratory chain are uncertain. Although the random diffusion model [C.R. Hackenbrock, B. Chazotte, S.S. Gupte, The random collision model and a critical assessment of diffusion and collision in mitochondrial electron transport, J. Bioenerg. Biomembranes 18 (1986) 331-368] has been widely accepted, recent evidence suggests the presence of supramolecular aggregates. In particular, evidence for a Complex I-Complex III supercomplex stems from both structural and kinetic studies. Electron transfer in the supercomplex may occur by electron channelling through bound Coenzyme Q in equilibrium with the pool in the membrane lipids. The amount and nature of the lipids modify the aggregation state and there is evidence that lipid peroxidation induces supercomplex disaggregation. Another important aspect in Complex I is its capacity to reduce oxygen with formation of superoxide anion. The site of escape of the single electron is debated and either FMN, iron-sulphur clusters, and ubisemiquinone have been suggested. The finding in our laboratory that two classes of hydrophobic inhibitors have opposite effects on superoxide production favours an iron-sulphur cluster (presumably N2) is the direct oxygen reductant. The implications in human pathology of better knowledge on these aspects of Complex I structure and function are briefly discussed.