Four decades of proteasome research have yielded extensive information on ubiquitin-dependent proteolysis. The archetype of proteasomes is a 20S barrel-shaped complex that does not rely on ubiquitin as a degradation signal but can degrade substrates with a considerable unstructured stretch. Since roughly half of all proteasomes in most eukaryotic cells are free 20S complexes, ubiquitin-independent protein degradation may coexist with ubiquitin-dependent degradation by the highly regulated 26S proteasome. This article reviews recent advances in our understanding of the biochemical and structural features that underlie the proteolytic mechanism of 20S proteasomes. The two outer α-rings of 20S proteasomes provide a number of potential docking sites for loosely folded polypeptides. The binding of a substrate can induce asymmetric conformational changes, trigger gate opening, and initiate its own degradation through a protease-driven translocation mechanism. Consequently, the substrate translocates through two additional narrow apertures augmented by the β-catalytic active sites. The overall pulling force through the two annuli results in a protease-like unfolding of the substrate and subsequent proteolysis in the catalytic chamber. Although both proteasomes contain identical β-catalytic active sites, the differential translocation mechanisms yield distinct peptide products. Non-overlapping substrate repertoires and product outcomes rationalize cohabitation of both proteasome complexes in cells.