In eukaryotic cells, proteasomes are highly conserved protease complexes and eliminate unwanted proteins which are marked by poly-ubiquitin chains for degradation. The 26S proteasome consists of the proteolytic core particle, the 20S proteasome, and the 19S regulatory particle, which are composed of 14 and 19 different subunits, respectively. Proteasomes are the second-most abundant protein complexes and are continuously assembled from inactive precursor complexes in proliferating cells. The modular concept of proteasome assembly was recognized in prokaryotic ancestors and applies to eukaryotic successors. The efficiency and fidelity of eukaryotic proteasome assembly is achieved by several proteasome-dedicated chaperones that initiate subunit incorporation and control the quality of proteasome assemblies by transiently interacting with proteasome precursors. It is important to understand the mechanism of proteasome assembly as the proteasome has key functions in the turnover of short-lived proteins regulating diverse biological processes.