Platinum-based antitumor agents have been effective in the treatments of many human malignancies but the ultimate success of these agents is often compromised by development of drug resistance. One mechanism associated with resistance to platinum drugs is reduced intracellular accumulation owing to impaired drug intake, enhanced outward transport, or both. Mechanisms for transporting platinum drugs were not known until recent demonstrations that import and export transporters involved in maintenance copper homeostasis are also involved in the transport of these drugs. Ctr1, the major copper influx transporter, has been convincingly demonstrated to transport cisplatin and its analogues, carboplatin, and oxaliplatin. Evidence also suggests that the two copper efflux transporters ATP7A and ATP7B regulate the efflux of cisplatin. These observations are intriguing, because conventional thinking of the inorganic physiologic chemistry of cisplatin and copper is quite different. Hence, understanding the underlying mechanistic aspects of these transporters is critically important. While the mechanisms by which hCtr1, ATP7A and ATP7B transport copper ions have been studied extensively, very little is known about the mechanisms by which these transporters shuffle platinum-based antitumor agents. This review discusses the identification of copper transporters as platinum drug transporters, the structural-functional and mechanistic aspects of these transporters, the mechanisms that regulate their expression, and future research directions that may eventually lead to improved efficacy of platinum-based-based drugs in cancer chemotherapy through modulation of their transporters’ activities.