This perspective is partly review and partly proposal. N-degrons and C-degrons are degradation signals whose main determinants are, respectively, the N-terminal and C-terminal residues of cellular proteins. Ndegrons and C-degrons include, to varying extents, adjoining sequence motifs, and also internal lysine residues that function as polyubiquitylation sites. Discovered in 1986, N-degrons were the first degradation signals in short-lived proteins. A particularly large set of C-degrons was discovered in 2018. We describe multifunctional proteolytic systems that target N-degrons and C-degrons. We also propose to denote these systems as "N-degron pathways" and "C-degron pathways." The former notation replaces the earlier name "N-end rule pathways." The term "N-end rule" was introduced 33 years ago, when only some N-terminal residues were thought to be destabilizing. However, studies over the last three decades have shown that all 20 amino acids of the genetic code can act, in cognate sequence contexts, as destabilizing N-terminal residues. Advantages of the proposed terms include their brevity and semantic uniformity for N-degrons and C-degrons. In addition to being topologically analogous, N-degrons and C-degrons are related functionally. A proteolytic cleavage of a subunit in a multisubunit complex can create, at the same time, an Ndegron (in a C-terminal fragment) and a spatially adjacent C-degron (in an N-terminal fragment). Consequently, both fragments of a subunit can be selectively destroyed through attacks by the N-degron and C-degron pathways.The lifespans of protein molecules in a cell range from less than a minute to many days. Regulated protein degradation protects cells from misfolded, aggregated, or otherwise abnormal proteins, and also controls the levels of proteins that evolved to be short-lived in vivo. Some proteolytic pathways can selectively destroy a specific subunit of a protein complex. Such pathways can act as proteinremodeling devices (1). They can either activate or inactivate a protein machine, change its enzymatic specificity, alter its subunit composition, or repair an oligomeric complex, for example, by destroying fragments of a cleaved subunit that are still embedded in the complex. This would allow a replacement of the cleaved subunit by its intact counterpart. Many biological transitions involve remodeling of protein complexes through subunit-selective degradation, in settings that range from cell-division cycles and circadian circuits to cell differentiation and responses to stresses.One function of protein degradation is the quality control of nascent and newly formed proteins. Selective proteolysis eliminates those proteins (including mutant ones) that fold too slowly, misfold, or do not satisfy other requirements of quality control. Most proteins function as multisubunit complexes, which often assemble cotranslationally. Quality-control systems destroy subunits that are either overproduced relative to other subunits of a complex or do not become incorporated into a complex rapi...