Eukaryotic 20S proteasomes harbor a remarkably complex architecture and unique proteolytic properties. Its catalytic mechanism places this enzyme in a new kind of protease family, The recently solved crystal structure of the yeast 20S complex, along with elucidation of the maturation pathway of human proteasomes, has allowed insight into structure/function relationships, Although not all of the unusual enzymatic properties such as broad substrate specificity, predominant generation of peptides with a specific size, or susceptibility to activating complexes can be explained in detail, knowledge of the structure provides important hints for an explanation of underlying mechanisms, Except for ribosome biogenesis, the complexity of eukaryotic proteasome maturation is without precedence, It is a slow process that involves a series of precisely ordered events, Proteasome structure formation is characterized by an initial cooperative formation of an alpha ring matrix, providing docking sites for a defined subset of beta subunits, Subsequent structural rearrangement allows the residual subunits to bind, followed by dimerization of two half-proteasomes, The prosequences of beta subunits exert specific functions during this process and are removed by cis and trans-autocatalysis, most likely in the completely assembled proteasome cylinder.