To control the quality of RNA biogenesis in the nucleus, cells use sophisticated molecular machines. These machines recognize and degrade not only RNA trimmings--the leftovers of RNA processing--but also incorrectly processed RNAs that contain defects. By using this mechanism, cells ensure that only high-quality RNAs are engaged in protein synthesis and other cellular processes. The exosome--a complex of several exoribonucleolytic and RNA-binding proteins--is the central 3'-end RNA degradation and processing factor in this surveillance apparatus. The exosome operates with auxiliary factors that stimulate its activity and recruit its RNA substrates in the crowded cellular environment. In this review, we discuss recent structural and functional data related to the nuclear quality-control apparatus, including the long-awaited structure of the human exosome and its activity.