Drug resistance continues to be a major factor in limiting the effectiveness of cancer chemotherapy. Evidence from a variety of sources implicates a genetic basis for most drug-resistant phenotypes. Assuming a random spontaneous origin for these resistant cells, it is possible to develop mathematical and computer-based models of the drug treatment of tumors. These can provide a more intuitive understanding of the basis of treatment success or failure. This in turn may lead to the development of more rational and effective treatment protocols. Studies of phenomena such as pleiotropic drug resistance are providing insights into how multiple levels of drug resistance occur and are yielding information on how certain types of drug resistance may be prevented or overcome.