Irreversible binding is usually associated with the formation of a covalent bond between the inhibitor and a residue in the enzyme active site. The study of high-affinity, irreversible, and slowly binding enzyme inhibitors presents complications that are often overlooked; as a consequence, puzzling information abounds in the literature. This chapter begins with a classification of these types of inhibitors; each type is then treated separately, but the classification is not exclusive and the same inhibitor may belong to two or more classes. It presents more refined tests and a basic treatment of slowly equilibrating and irreversible inhibitors. Rapidly binding irreversible inhibitors require minimal or no incubation with the enzyme to bind and to form an irreversible complex. Mechanism-based enzyme inhibitors are molecules that are transformed by the enzyme, like substrates, but form a reactive intermediate that may or may not react with amino acid residues of the catalytic site and inactivate the enzyme.