Discovery of the evolutionary conserved RNA exosome was a milestone in RNA biology. First identified as an activity essential for the processing of ribosomal RNA, the exosome has since proved to be central for RNA processing and degradation in both the nucleus and the cytoplasm of eukaryotic cells. This multisubunit protein complex consists of a catalytically inert 9-subunit core endowed with associated ribonucleolytic activities and further assisted by compartment-specific cofactors required for its activation and substrate targeting. Although many features of exosome biology are known, fundamental aspects are still under investigation. In this chapter, we review current biochemical and functional knowledge of eukaryotic exosomes. After introducing some of their nuclear and cytoplasmic functions, we discuss the structural organization and evolutionary aspects of exosome complexes. Finally, we describe catalytic properties of the complex and its regulation by cofactors.