γ-Glutamyl moiety that is attached to the cysteine (Cys) residue in glutathione (GSH) protects it from peptidase-mediated degradation. The sulfhydryl group of the Cys residue represents most of the functions of GSH, which include electron donation to peroxidases, protection of reactive sulfhydryl in proteins via glutaredoxin, and glutathione conjugation of xenobiotics, whereas Cys-derived sulfur is also a pivotal component of some redox-responsive molecules. The amount of Cys that is available tends to restrict the capacity of GSH synthesis. In in vitro systems, cystine is the major form in the extracellular milieu, and a specific cystine transporter, xCT, is essential for survival in most lines of cells and in many primary cultivated cells as well. A reduction in the supply of Cys causes GPX4 to be inhibited due to insufficient GSH synthesis, which leads to iron-dependent necrotic cell death, ferroptosis. Cells generally cannot take up GSH without the removal of γ-glutamyl moiety by γ-glutamyl transferase (GGT) on the cell surface. Meanwhile, the Cys–GSH axis is essentially common to certain types of cells; primarily, neuronal cells that contain a unique metabolic system for intercellular communication concerning γ-glutamyl peptides. After a general description of metabolic processes concerning the Cys–GSH axis, we provide an overview and discuss the significance of GSH-related compounds in the nervous system.