Tumor necrosis factor receptor-associated protein 1 (TRAP1) is a mitochondrial molecular chaperone modulating cellular metabolism and signaling pathways by altering the conformation, activity, and stability of numerous substrate proteins called clients. It exerts its chaperone function as an adaptive response to counter cellular stresses instead of maintaining housekeeping protein homeostasis. However, the stress-adaptive machinery becomes dysregulated to support the progression and maintenance of human diseases, such as cancers; therefore, TRAP1 has been proposed as a promising target protein for anticancer drug development. In this review, by collating recent reports on high-resolution TRAP1 structures and structure-activity relationships of inhibitors, we aimed to provide better insights into the chaperoning mechanism of the emerging drug target and to suggest an efficient strategy for the development of potent TRAP1 inhibitors.