Biological nitrogen fixation, catalyzed by nitrogenases, contributes about half of the nitrogen needed to global agriculture. For forty years synthetic chemists and theoreticians have tried to understand and model the structure and function of this important metalloenzyme. Ten years after the first report on the crystal structure of the MoFe protein, scientists still have not been able to synthesize a chemical equivalent of the FeMo cofactor nor the structure knowledge revealed the key to its catalytic activity. This paper with 104 references presents a review of the most relevant advances in chemical nitrogen fixation and their relation with the nitrogenases.