The proteasome is an intricate molecular machine, which serves to degrade proteins following their conjugation to ubiquitin. Substrates dock onto the proteasome at its 19-subunit regulatory particle via a diverse set of ubiquitin receptors and are then translocated into an internal chamber within the 28-subunit proteolytic core particle (CP), where they are hydrolyzed. Substrate is threaded into the CP through a narrow gated channel, and thus translocation requires unfolding of the substrate. Six distinct ATPases in the regulatory particle appear to form a ring complex and to drive unfolding as well as translocation. ATP-dependent, degradation-coupled deubiquitination of the substrate is required both for efficient substrate degradation and for preventing the degradation of the ubiquitin tag. However, the proteasome also contains deubiquitinating enzymes (DUBs) that can remove ubiquitin before substrate degradation initiates, thus allowing some substrates to dissociate from the proteasome and escape degradation. Here we examine the key elements of this molecular machine and how they cooperate in the processing of proteolytic substrates.