Tumor necrosis factor receptor-associated protein 1 (TRAP1), also known as heat shock protein 75 (HSP75), is a member of the heat shock protein 90 (HSP90) chaperone family that resides mainly in the mitochondria. As a mitochondrial molecular chaperone, TRAP1 supports protein folding and contributes to the maintenance of mitochondrial integrity even under cellular stress. TRAP1 is a cellular regulator of mitochondrial bioenergetics, redox homeostasis, oxidative stress-induced cell death, apoptosis, and unfolded protein response (UPR) in the endoplasmic reticulum (ER). TRAP1 has attracted increasing interest as a therapeutical target, with a special focus on the design of TRAP1 specific inhibitors. Although TRAP1 was extensively studied in the oncology field, its role in central nervous system cells, under physiological and pathological conditions, remains largely unknown. In this review, we will start by summarizing the biology of TRAP1, including its structure and related pathways. Thereafter, we will continue by debating the role of TRAP1 in the maintenance of redox homeostasis and protection against oxidative stress and apoptosis. The role of TRAP1 in neurodegenerative disorders will also be discussed. Finally, we will review the potential of TRAP1 inhibitors as neuroprotective drugs.