The identification and characterization of the exosome complex has shown that the exosome is a complex of 3' --> 5' exoribonucleases that plays a key role in the processing and degradation of a wide variety of RNA substrates. Advances in the understanding of exosome function have led to the identification of numerous cofactors that are required for a selective recruitment of the exosome to substrate RNAs, for their structural alterations to facilitate degradation, and to aid in their complete degradation/processing. Structural data obtained by two-hybrid interaction analyses and X-ray crystallography show that the core of the exosome adopts a doughnut-like structure and demonstrates that probably not all exosome subunits are active exoribonucleases. Despite all data obtained on the structure and function of the exosome during the last decade, there are still a lot of unanswered questions. What is the molecular mechanism by which cofactors select and target substrate RNAs to the exosome and modulate its function for correct processing or degradation? How can the exosome discriminate between processing or degradation of a specific substrate RNA? What is the precise structure of exosome subunits and how do they contribute to its function? Here we discuss studies that provide some insight to these questions and speculate on the mechanisms that control the exosome.