The proteasome inhibitors of this invention are peptide-based compounds with a short linear sequence of amino acids. A cyclic oxo or thio group is attached to the N terminal amino acid. A protein-reactive electrophilic group such as an epoxyketone, an aziridinylketones, or a beta lactone is attached to the C terminal amino acid. Upon contact with a proteasome complex in a target cell, the electrophilic group reacts with a functional group in or near a binding pocket or active site of the proteasome, forming a covalent bond and thereby inactivating the proteasome. These and other proteasome inhibitors can be screened for inhibition activity and an ability to selectively eliminate senescent cells or cancer cells. Compounds with the requisite activity can be developed for the treatment of conditions such as osteoarthritis, ophthalmic disease, pulmonary disease, and atherosclerosis.