A large body of structural work conducted over the past ten years has elucidated mechanistic details related to 3' to 5' processing and decay of RNA substrates by the RNA exosome. This chapter will focus on the structural organization of eukaryotic exosomes and their evolutionary cousins in bacteria and archaea with an emphasis on mechanistic details related to substrate recognition and to 3' to 5' phosphorolytic exoribonucleolytic activities of bacterial and archaeal exosomes as well as the hydrolytic exoribonucleolytic and endoribonucleolytic activities of eukaryotic exosomes. These points will be addressed in large part through presentation of crystal structures of phosphorolytic enzymes such as bacterial RNase PH, PNPase and archaeal exosomes and crystal structures of the eukaryotic exosome and exosome sub-complexes in addition to standalone structures of proteins that catalyze activities associated with the eukaryotic RNA exosome, namely Rrp44, Rrp6 and their bacterial counterparts.