Proteasomes are highly conserved protease complexes responsible for the degradation of aberrant and short-lived proteins. In highly proliferating yeast and mammalian cells, proteasomes are predominantly nuclear. During quiescence and cell cycle arrest, proteasomes accumulate in granules in close proximity to the nuclear envelope/ER. With prolonged quiescence in yeast, these proteasome granules pinch off as membraneless organelles, and migrate as stable entities through the cytoplasm. Upon exit from quiescence, the proteasome granules clear and the proteasomes are rapidly transported into the nucleus, a process reflecting the dynamic nature of these multisubunit complexes. Due to the scarcity of studies on the nuclear transport of mammalian proteasomes, we summarised the current knowledge on the nuclear import of yeast proteasomes. This pathway uses canonical nuclear localisation signals within proteasomal subunits and Srp1/Kap95, and the canonical import receptor, named importin/karyopherin αβ. Blm10, a conserved 240 kDa protein, which is structurally related to Kap95, provides an alternative import pathway. Two models exist upon which either inactive precursor complexes or active holo-enzymes serve as the import cargo. Here, we reconcile both models and suggest that the import of inactive precursor complexes predominates in dividing cells, while the import of mature enzymes mainly occurs upon exit from quiescence.