Ubiquitin Proteasome System (UPS) is an adaptable and finely tuned system that sustains proteostasis network under a large variety of physiopathological conditions. Its dysregulation is often associated with the onset and progression of human diseases; hence, UPS modulation has emerged as a promising new avenue for the development of treatments of several relevant pathologies, such as cancer and neurodegeneration. The clinical interest in proteasome inhibition has considerably increased after the FDA approval in 2003 of bortezomib for relapsed/refractory multiple myeloma, which is now used in the front-line setting. Thereafter, two other proteasome inhibitors (carfilzomib and ixazomib), designed to overcome resistance to bortezomib, have been approved for treatment-experienced patients, and a variety of novel inhibitors are currently under preclinical and clinical investigation not only for haematological malignancies but also for solid tumours. However, since UPS collapse leads to toxic misfolded proteins accumulation, proteasome is attracting even more interest as a target for the care of neurodegenerative diseases, which are sustained by UPS impairment. Thus, conceptually, proteasome activation represents an innovative and largely unexplored target for drug development. According to a multidisciplinary approach, spanning from chemistry, biochemistry, molecular biology to pharmacology, this review will summarize the most recent available literature regarding different aspects of proteasome biology, focusing on structure, function and regulation of proteasome in physiological and pathological processes, mostly cancer and neurodegenerative diseases, connecting biochemical features and clinical studies of proteasome targeting drugs.