Abstract: Proteasomes are large multicatalytic protease complexes found in the cytoplasm and nucleus of all eukaryotic cells. 20S proteasomes are cylindrically shaped particles composed of a set of different subunits arranged in a stack of 4 rings with 7-fold symmetry. In yeast 14 different genes are known, which are proposed to code for the complete set of 20S proteasomal subunits. They can be divided in 7 alpha- and 7 beta-type subunits. 26S proteasomes are even larger proteinase complexes which contain the 20S proteasome as the functional proteolytic core. They degrade ubiquitinylated proteins in vitro. Several yeast 26S proteasome subunits have been characterized as members of a novel ATPase family. Studies with yeast 20S and 26S proteasome mutants uncovered the function of proteasomes in stress-dependent and ubiquitin-mediated proteolytic pathways. Proteasomes are important for cellular regulation, cell differentiation, adaptation to environmental changes and are involved in cell cycle control.