The proteasome is a cellular protease responsible for the selective degradation of the majority of the intracellular proteome. It recognizes, unfolds, and cleaves proteins that are destined for removal, usually by prior attachment to polymers of ubiquitin. This macromolecular machine is composed of two subcomplexes, the 19S regulatory particle (RP) and the 20S core particle (CP), which together contain at least 33 different and precisely positioned subunits. How these subunits assemble into functional complexes is an area of active exploration. Here we describe the current status of studies on the assembly of the 20S proteasome (CP). The 28-subunit CP is found in all three domains of life and its cylindrical stack of four heptameric rings is well conserved. Though several CP subunits possess self-assembly properties, a consistent theme in recent years has been the need for dedicated assembly chaperones that promote on-pathway assembly. To date, a minimum of three accessory factors have been implicated in aiding the construction of the 20S proteasome. These chaperones interact with different assembling proteasomal precursors and usher subunits into specific slots in the growing structure. This review will focus largely on chaperone-dependent CP assembly and its regulation.