The RNA exosome complex is the most versatile RNA-degradation machine in eukaryotes. The exosome has a central role in several aspects of RNA biogenesis, including RNA maturation and surveillance. Moreover, it is emerging as an important player in regulating the expression levels of specific mRNAs in response to environmental cues and during cell differentiation and development. Although the mechanisms by which RNA is targeted to (or escapes from) the exosome are still not fully understood, general principles have begun to emerge, which we discuss in this Review. In addition, we introduce and discuss novel, previously unappreciated functions of the nuclear exosome, including in transcription regulation and in the maintenance of genome stability.