The proteasome, a multisubunit, multicatalytic proteinase complex, is attracting growing attention as the main intracellular, extralysosomal, proteolytic system involved in ubiquitin-(Ub) dependent and Ub-independent intracellular proteolysis. Its involvement in the mitotic cycle, and control of the half-life of most cellular proteins, functions absolutely necessary for cell growth and viability, make it an attractive target for researchers of intracellular metabolism and an important target for pharmacological intervention. The proteasome belongs to a new mechanistic class of proteases, the N-terminal nucleophile hydrolases, where the N-terminal threonine residue functions as the nucleophile. This minireview focuses on the three classical catalytic activities of the proteasome, designated chymotrypsin-like, trypsin-like, and peptidyl-glutamyl-peptide hydrolyzing in eukaryotes and also the activities of the more simple Archaebacteria and Eubacteria proteasomes. Other catalytic activities of the proteasome and their possible origin are also examined. The specificity of the catalytic components toward synthetic substrates, natural peptides, and proteins and their relationship to the catalytic centers are reviewed. Some unanswered questions and future research directions are suggested.