Four membered b-lactam rings do not show unusual reactivity compared with their acyclic amide analogues and there is no evidence of concerted mechanisms for nucleophilic substitution reactions at the carbonyl centre. The identity of the general base/acid catalyst in the serine b-lactamases, which catalyse the hydrolysis of b-lactams, is unknown. There are no ideal transition state analogue inhibitors for these enzymes which involve several intermediates and transition states. The class C serine b-lactamase enhances the rate of phosphonylation of its active site serine residue by a similar magnitude to the enzyme rate enhancement factor for the hydrolysis of b-lactams. Comparisons are made between the stereochemical consequences of tetrahedral and trigonal bipyramidal intermediates for hydrolysis and phosphonylation respectively. Class B zinc b-lactamases are inhibited by thiol dipeptides with a D configuration at the cysteine centre analogous to the L configuration at C6 in penicillins. The mechanism of hydrolysis catalysed by the metallo-b-lactamases probably involves a di-anionic tetrahedral intermediate stabilised by zinc(II).