Proteases are classified into six distinct classes (cysteine, serine, threonine, aspartic, glutamic, and metalloproteases) on the basis of catalytic mechanism. The cellular control of protein quality senses misfolded or damaged proteins principally by selective ubiquitin-proteasome pathway and non-selective autophagy-lysosome pathway. The two pathways do not only maintain cell homeostasis physiologically, but also mediate necrosis and apoptosis pathologically. Proteasomes are threonine proteases, whereas cathepsins are lysosomal aspartic proteases. Calpains are non-lysosomal cysteine proteases and calcium-dependent papain-like enzyme. Calpains and cathepsins are involved in the neuronal necrosis, which are accidental cell death. Necrosis is featured by the disruption of plasma membranes and lysosomes, the loss of ATP and ribosomes, the lysis of cell and nucleus, and the caspase-independent DNA fragmentation. On the other hand, caspases are cysteine endoproteases and mediate neuronal cell death such as apoptosis and pyroptosis, which are programmed cell death. In the central nervous system, necroptosis, ferroptosis and autophagic cell death are also classified into programmed cell death. Neuronal apoptosis is characterized by cell shrinkage, plasma membrane blebbing, karyorrhexis, chromatin condensation, and DNA fragmentation. Necroptosis and pyroptosis are necrotic and lytic forms of programmed cell death, respectively. Although autophagy is involved in cell survival, it fails to maintain cellular homeostasis, resulting in autophagic cell death. Ferroptosis is induced by reactive oxygen species in excitotoxicity of glutamate and ischemia-reperfusion. Apoptosis and pyroptosis are dependent on caspase-3 and caspase-1, respectively. Autophagic cell death and necroptosis are dependent on calpain and cathepsin, respectively, but independent of caspase. Although apoptosis has been defined by the absence of morphological features of necrosis, the two deaths are both parts of a continuum. The intracellular proteases do not only maintain cell homeostasis but also regulate neuronal maturation during the development of embryonic brain. Furthermore, neurodegenerative diseases are caused by the impairment of quality control mechanisms for a proper folding and function of protein.