Proteasomes are ring- or cylinder-shaped particles that have a sedimentation coefficient of 20S and are composed of a characteristic set of small polypeptides. These particles have a latent multicatalytic proteinase activity. Recently, proteasomes were found to combine reversibly with multiple protein components to form 26S proteolytic complexes that catalyze ATP-dependent, selective breakdown of proteins ligated with ubiquitin. This suggests that the 26S complexes are a new type of ATP-requiring protease in eukaryotic cells. We have studied the structures of various eukaryotic proteasomes at the molecular level by physicochemical and recombinant DNA techniques and have proposed that the gross structures of proteasomes, such as their size and shape, have been highly conserved during evolution. Proteasome subunits appear to be encoded by a family of homologous genes named the "proteasome gene family," which may have evolved from a common ancestral gene. Evidence obtained by genetic analyses in yeast and studies on the levels of proteasome expression in various eukaryotic cells indicates that proteasomes have essential roles in the cell. In this review, we summarize available information on the protein and gene structures of proteasomes and discuss the biological functions of proteasomes.