Proteasomes are large supramolecular protein complexes present in all prokaryotic and eukaryotic cells, where they perform targeted degradation of intracellular proteins. Until recently, it was generally accepted that prior proteolytic degradation in proteasomes the proteins had to be targeted by ubiquitination: the ATP-dependent addition of (typically four sequential) residues of the low-molecular ubiquitin protein, involving the ubiquitin-activating enzyme, ubiquitin-conjugating enzyme and ubiquitin ligase. The cytoplasm and nucleoplasm proteins labeled in this way are then digested in 26S proteasomes. However, in recent years it has become increasingly clear that using this route the cell eliminates only a part of unwanted proteins. Many proteins can be cleaved by the 20S proteasome in an ATP-independent manner and without previous ubiquitination. Ubiquitin-independent protein degradation in proteasomes is a relatively new area of studies of the role of the ubiquitin-proteasome system. However, recent data obtained in this direction already correct existing concepts about proteasomal degradation of proteins and its regulation. Ubiquitin-independent proteasome degradation needs the main structural precondition in proteins: the presence of unstructured regions in the amino acid sequences that provide interaction with the proteasome. Taking into consideration that in humans almost half of all genes encode proteins that contain a certain proportion of intrinsically disordered regions, it appears that the list of proteins undergoing ubiquitin-independent degradation will demonstrate further increase. Since 26S of proteasomes account for only 30% of the total proteasome content in mammalian cells, most of the proteasomes exist in the form of 20S complexes. The latter suggests that ubiquitin-independent proteolysis performed by the 20S proteasome is a natural process of removing damaged proteins from the cell and maintaining a constant level of intrinsically disordered proteins. In this case, the functional overload of proteasomes in aging and/or other types of pathological processes, if it is not accompanied by triggering more radical mechanisms for the elimination of damaged proteins, organelles and whole cells, has the most serious consequences for the whole organism.