It is generally accepted that recent advances in anticancer agents have contributed significantly to the improvement of both the disease-free survival and quality of life in cancer patients. However, in many instances, a favorable initial response to treatment changes afterwards, thereby leading to cancer relapse and recurrence. This phenomenon of acquired resistance to therapy, it is a major problem for totally efficient anticancer therapy. The failure to obtain an initial response reflects a form of intrinsic resistance. Specific cell membrane transporter proteins are implicated in intrinsic drug resistance by altering drug transport and pumping drugs out of the tumor cells. Moreover, the gradual acquisition of specific genetic and epigenetic abnormalities in cancer cells could contribute greatly to acquired drug resistance. A critical issue in the clinical setting, is that the problem of drug resistance appears to have a negative effect on also the new molecularly-targeted anticancer drugs. Several ongoing efforts are being made by the medical community aimed to the identification of such resistance mechanisms and the development of novel drugs that could overcome them. In this review, the major drug resistance mechanisms and strategies to overcome them are critically discussed, and also possible future directions are suggested.