The ubiquitin-proteasome system is a master regulator of protein homeostasis, by which proteins are initially targeted for poly-ubiquitination by E3 ligases and then degraded into short peptides by the proteasome. Nature evolved diverse peptidic motifs, termed degrons, to signal substrates for degradation. We discuss degrons of the N-end rule pathway and also degrons characterized by post-translational modifications, including phosphorylation and hydroxylation. In each case we detail the structural basis of E3 ligase:degron recognition and small-molecule mimicry approaches that disrupt those protein-protein interactions. We present as well genetic and chemical technologies that enable targeted degradation of proteins of interest, namely small-molecule dependent inducible degrons and chemical degraders, e.g. proteolysis-targeting chimeras (PROTACs).