For many years, the ubiquitin-26S proteasome degradation pathway was considered the primary route for proteasomal degradation. However, it is now becoming clear that proteins can also be targeted for degradation by the core 20S proteasome itself. Degradation by the 20S proteasome does not require ubiquitin tagging or the presence of the 19S regulatory particle; rather, it relies on the inherent structural disorder of the protein being degraded. Thus, proteins that contain unstructured regions due to oxidation, mutation, or aging, as well as naturally, intrinsically unfolded proteins, are susceptible to 20S degradation. Unlike the extensive knowledge acquired over the years concerning degradation by the 26S proteasome, relatively little is known about the means by which 20S-mediated proteolysis is controlled. Here, we describe our current understanding of the regulatory mechanisms that coordinate 20S proteasome-mediated degradation, and highlight the gaps in knowledge that remain to be bridged.