An increasing wealth of data indicates a close relationship between the presynaptic protein alpha-synuclein and Parkinson’s disease (PD) pathogenesis. Alpha-synuclein protein levels are considered as a major determinant of its neurotoxic potential, whereas secreted extracellular alpha-synuclein has emerged as an additional important factor in this regard. However, the manner of alpha-synuclein degradation in neurons remains contentious. Both the ubiquitin–proteasome system (UPS) and the autophagy–lysosome pathway (ALP)—mainly macroautophagy and chaperone-mediated autophagy—have been suggested to contribute to alpha-synuclein turnover. Additionally, other proteases such as calpains, neurosin, and metalloproteinases have been also proposed to have a role in intracellular and extracellular alpha-synuclein processing. Both UPS and ALP activity decline with aging and such decline may play a pivotal role in many neurodegenerative conditions. Alterations in these major proteolytic pathways may result in alpha-synuclein accumulation due to impaired clearance. Conversely, increased alpha-synuclein protein burden promotes the generation of aberrant species that may impair further UPS or ALP function, generating thus a bidirectional positive feedback loop leading to neuronal death. In the current review, we summarize the recent findings related to alpha-synuclein degradation, as well as to alpha-synuclein-mediated aberrant effects on protein degradation systems. Identifying the factors that regulate alpha-synuclein association to cellular proteolytic pathways may represent potential targets for therapeutic interventions in PD and related synucleinopathies.