How does the enzyme nitrogenase reduce the inert molecule N2 to NH3 under ambient conditions that are so different from the energy-expensive conditions of the best industrial practices? This review focuses on recent theoretical investigations of the catalytic site, the iron-molybdenum cofactor FeMo-co, and the way in which it is hydrogenated by protons and electrons and then binds N2. Density functional calculations provide reaction profiles and activation energies for possible mechanistic steps. This establishes a conceptual framework and the principles for the coordination chemistry of FeMo-co that are essential to the chemical mechanism of catalysis. The model advanced herein explains relevant experimental data.