Nitrile hydratase, the enzyme involved in microbial nitrile assimilation, comprises either one non-heme low-spin iron(III) or a non-corrinoid cobalt(III) center at the active site. Two carboxamido nitrogens, one cysteine-sulfur, and two sulfurs from a cysteine-sulfenic (Cys-SO) and a cysteine-sulfinic (Cys-SO2) acid moiety respectively constitute the donor set around the metal center of this hydrolytic enzyme. Binding of one molecule of NO at the sixth site of the iron(III) center modulates the activity of the enzyme. It is suggested that a metal-bound hydroxide could be involved in the hydration of nitriles. Attack of water (or hydroxide) on a metal-bound nitrile is another possibility. During the past few years, modeling work by several groups have provided a great deal of insight into the structure and function of nitrile hydratase. Structural and spectroscopic studies on iron(III) and cobalt(III) complexes of various designed S,N-containing ligands have shown that the unusual coordination structure of the M(III) site (a) raises its potential and shuts off any redox activity, (b) allows binding of NO at the sixth site and oxidative modification of the bound S donors, and (c) brings the pKa of metal-bound water close to 7. Attempts to synthesize catalytically active model complexes have met with limited success. This review includes the results and implications of the modeling studies reported so far.