The importance of platinum drugs in cancer chemotherapy is underscored by the clinical success of cisplatin [cis-diamminedichloroplatinum(II)] and its analogues and by clinical trials of other, less toxic platinum complexes that are active against resistant tumors. The antitumor effect of platinum complexes is believed to result from their ability to form various types of adducts with DNA. Nevertheless, drug resistance can occur by several ways: increased drug efflux, drug inactivation, alterations in drug target, processing of drug-induced damage, and evasion of apoptosis. This review focuses on mechanisms of resistance and sensitivity of tumors to conventional cisplatin associated with DNA modifications. We also discuss molecular mechanisms underlying resistance and sensitivity of tumors to the new platinum compounds synthesized with the goal to overcome resistance of tumors to established platinum drugs. Importantly, a number of new platinum compounds were designed to test the hypothesis that there is a correlation between the extent of resistance of tumors to these agents and their ability to induce a certain kind of damage or conformational change in DNA. Hence, information on DNA-binding modes, as well as recognition and repair of DNA damage is discussed, since this information may be exploited for improved structure-activity relationships.