The proteasome is the major ATP-dependent protease in eukaryotic cells, but limited structural information restricts a mechanistic understanding of its activities. The proteasome regulatory particle, consisting of the lid and base subcomplexes, recognizes and processes polyubiquitinated substrates. Here we used electron microscopy and a new heterologous expression system for the lid to delineate the complete subunit architecture of the regulatory particle from yeast. Our studies reveal the spatial arrangement of ubiquitin receptors, deubiquitinating enzymes and the protein unfolding machinery at subnanometre resolution, outlining the substrate's path to degradation. Unexpectedly, the ATPase subunits within the base unfoldase are arranged in a spiral staircase, providing insight into potential mechanisms for substrate translocation through the central pore. Large conformational rearrangements of the lid upon holoenzyme formation suggest allosteric regulation of deubiquitination. We provide a structural basis for the ability of the proteasome to degrade a diverse set of substrates and thus regulate vital cellular processes.