The proteasome is a highly sophisticated protease complex designed to carry out selective, efficient and processive hydrolysis of client proteins. It is known to collaborate with ubiquitin, which polymerizes to form a marker for regulated proteolysis in eukaryotic cells. The highly organized proteasome plays a prominent role in the control of a diverse array of basic cellular activities by rapidly and unidirectionally catalyzing biological reactions. Studies of the proteasome during the past quarter of a century have provided profound insights into its structure and functions, which has appreciably contributed to our understanding of cellular life. Many questions, however, remain to be elucidated.