The development of resistance in mammalian cells to toxic drugs is a significant clinical problem, especially in cancer chemotherapy where drug-resistant tumor cells often prove to be refractory to treatment. In this article, we review some of the basic mechanisms of drug resistance from the perspective of a single cell bathed in medium containing the drug. These mechanisms may be categorized according to changes in the cell that affect the ability of the drug to accumulate intracellularly, changes in enzymes that are required for drug toxicity, alterations in trapping of the drug or detoxification of the drug, alterations in binding to an intracellular target, or alterations in cellular processes that compensate for the action of the drug. This latter mechanism is illustrated in some depth by discussing mutants of Chinese hamster ovary cells that are resistant to the effects of drugs that interfere with microtubule assembly.