Most RNAs in eukaryotic cells are produced as precursors that undergo processing at the 3′ and/or 5′ end to generate the mature transcript. In addition, many transcripts are degraded not only as part of normal recycling, but also when recognized as aberrant by the RNA surveillance machinery. The exosome, a conserved multiprotein complex containing two nucleases, is involved in both the 3′ processing and the turnover of many RNAs in the cell. A series of factors, including the TRAMP (Trf4–Air2–Mtr4 polyadenylation) complex, Mpp6 and Rrp47, help to define the targets to be processed and/or degraded and assist in exosome function. The majority of the data on the exosome and RNA maturation/decay have been derived from work performed in the yeast Saccharomyces cerevisiae. In the present paper, we provide an overview of the exosome and its role in RNA processing/degradation and discuss important new insights into exosome composition and function in human cells.