The eukaryotic RNA exosome is an essential and conserved protein complex that can degrade or process RNA substrates in the 3’ to 5’ direction. The nuclear RNA exosome includes a non-catalytic donut-shaped core (Exo9) that binds Dis3 (aka Rrp44) and the Rrp6/Rrp47 heterodimer to modulate their processive and distributive exoribonuclease activities, respectively. Additionally, cofactor proteins such as Mpp6 and the TRAMP and Ski complexes assist the exosome in RNA decay in different subcellular compartments. Decades of study have revealed that the exosome acts on all classes of RNA in diverse model organisms and that the catalytic subunits primarily engage these substrates by first threading them through a prominent central channel in Exo9. Structural and biochemical studies have demonstrated that this channel is wide enough to permit single-stranded but not double-stranded RNA to enter, presenting an obstacle for degradation of structured substrates. This can be overcome by extension of the RNA 3’ end, which can be accomplished by the polyadenylation and RNA helicase activities of the nuclear TRAMP complex. Recruitment of TRAMP to the exosome and the interplay between the various activities contained within these complexes remain unclear due to lack of rigorous biochemical characterization. Contained within this dissertation are our efforts to investigate this important process, starting with structural characterization of the cofactor-less nuclear exosome (Exo9 plus Rrp6 and Dis3) in Chapter 1. Use of an engineered substrate enabled crystallization and X-ray structure determination of this complex, which uncovered features in the non-catalytic core that modulate Dis3’s activity in vitro. We also show that a 3’ phosphate containing RNA cannot be trimmed by Rrp6 and instead is fully degraded by Dis3. Chapters 2 and 3 concern recruitment of Mtr4, the TRAMP complex RNA helicase, to the exosome. In Chapter 2, we solve the crystal structure of the nuclear exosome bound to the cofactor Mpp6. Biochemical characterization of the Mpp6-exosome revealed that Mpp6, along with Rrp6/Rrp47, physically tethers Mtr4 to the complex and enables ATP-dependent degradation of structured substrates. Chapter 3 details preliminary work on structurally characterizing a substrate-loaded Mtr4-exosome complex using cryo-electron microscopy.