The ubiquitin-proteasome system is the major degradation pathway for short-lived proteins in eukaryotic cells. Targets of the ubiquitin-proteasome-system are proteins regulating a broad range of cellular processes including cell cycle progression, gene expression, the quality control of proteostasis and the response to geno- and proteotoxic stress. Prior to degradation, the proteasomal substrate is marked with a poly-ubiquitin chain. The key protease of the ubiquitin system is the proteasome. In dividing cells, proteasomes exist as holo-enzymes composed of regulatory and core particles. The regulatory complex confers ubiquitin-recognition and ATP dependence on proteasomal protein degradation. The catalytic sites are located in the proteasome core particle. Proteasome holo-enzymes are predominantly nuclear suggesting a major requirement for proteasomal proteolysis in the nucleus. In cell cycle arrested mammalian or quiescent yeast cells, proteasomes deplete from the nucleus and accumulate in granules at the nuclear envelope (NE) / endoplasmic reticulum (ER) membranes. In prolonged quiescence, proteasome granules drop off the NE / ER membranes and migrate as stable organelles throughout the cytoplasm, as thoroughly investigated in yeast. When quiescence yeast cells are allowed to resume growth, proteasome granules clear and proteasomes are rapidly imported into the nucleus.Here, we summarize our knowledge about the enigmatic structure of proteasome storage granules and the trafficking of proteasomes and their substrates between the cyto- and nucleoplasm.Most of our current knowledge is based on studies in yeast. Their translation to mammalian cells promises to provide keen insight into protein degradation in non-dividing cells which comprise the majority of our body’s cells.