Complex I (NADH:ubiquinone oxidoreductase) is a redox-driven proton pump that powers synthesis of adenosine triphosphate (ATP) and active transport in most organisms. This gigantic enzyme reduces quinone (Q) to quinol (QH2) in its hydrophilic domain, and transduces the released free energy into pumping of protons across its membrane domain, up to ca. 200 Å away from its active Q-reduction site. Recently resolved molecular structures of complex I from several species have made it possible for the first time to address the energetics and dynamics of the complete complex I using multi-scale methods of computational biochemistry. Here it is described how molecular simulations can provide important mechanistic insights into the function of the remarkable pumping machinery in complex I and stimulate new experiments.