Potent and selective inhibitors of matrix metalloproteinases (MMPs), a family of zinc proteases that can degrade all the components of the extracellular matrix, could be useful for treatment of diseases such as cancer and arthritis. The most potent MMP inhibitors are based on hydroxamate as zinc-binding group (ZBG). alpha-Arylsulfonylamino phosphonates incorporate a particularly favorable combination of phosphonate as ZBG and arylsulfonylamino backbone so that their affinity exceptionally attains the nanomolar strength frequently observed for hydroxamate analogues. The detailed mode of binding of [1-(4'-methoxybiphenyl-4-sulfonylamino)-2-methylpropyl]phosphonate has been clarified by the crystal structures of the complexes that the R- and S-enantiomers respectively form with MMP-8. The reasons for the preferential MMP-8 inhibition by the R-phosphonate are underlined and the differences in the mode of binding of analogous alpha-arylsulfonylamino hydroxamates and carboxylates are discussed.