Protein homeostasis or proteostasis is an essential balance of cellular protein levels mediated through an extensive network of biochemical pathways that regulate different steps of the protein quality control, from the synthesis to the degradation. All proteins in a cell continuously turn over, contributing to development, differentiation, and aging. Due to the multiple interactions and connections of proteostasis pathways, exposure to stress conditions may cause various types of protein damage, altering cellular homeostasis and disrupting the entire network with additional cellular stress. Furthermore, protein misfolding and/or alterations during protein synthesis results in inactive or toxic proteins, which may overload the degradation mechanisms. The maintenance of a balanced proteome, preventing the formation of impaired proteins, is accomplished by two major catabolic routes: the ubiquitin proteasomal system (UPS) and the autophagy-lysosomal system. The proteostasis network is particularly important in nondividing, long-lived cells, such as neurons, as its failure is implicated with the development of neurodegenerative diseases, such as Alzheimer’s disease, Parkinson’s disease, and amyotrophic lateral sclerosis. These neurological disorders share common risk factors such as aging, oxidative stress, environmental stress, and protein dysfunction, all of which alter cellular proteostasis, suggesting that general mechanisms controlling proteostasis may underlay the etiology of these diseases. In this review, we describe the major pathways of cellular proteostasis and discuss how their disruption contributes to the onset and progression of neurodegenerative diseases, focusing on the role of oxidative stress.