The proteasome is an essential component of the ATP-dependent proteolytic pathway in eukaryotic cells and is responsible for the degradation of most cellular proteins. The 20S (700-kDa) proteasome contains multiple peptidase activities that function through a new type of proteolytic mechanism involving a threonine active site. The 26S (2000-kDa) complex, which degrades ubiquitinated proteins, contains in addition to the 20S proteasome a 19S regulatory complex composed of multiple ATPases and components necessary for binding protein substrates. The proteasome has been highly conserved during eukaryotic evolution, and simpler forms are even found in archaebacteria and eubacteria. Major advances have been achieved recently in our knowledge about the molecular organization of the 20S and 19S particles, their subunits, the proteasome's role in MHC-class 1 antigen presentation, and regulators of its activities. This article focuses on recent progress concerning the biochemical mechanisms and intracellular functions of the 20S and 26S proteasomes.