Carbacephem β-lactam antibiotics having the following chemical structures (I) and (II) are disclosed: including stereoisomers, pharmaceutically acceptable salts, esters and prodrugs thereof, wherein Ar2, R1, R2 and R3 are as defined herein. The compounds are useful for the treatment of bacterial infections, in particular those caused by methicillin-resistant Staphylococcus spp.