Resistance to chemotherapy ('drug resistance') is a fundamental problem that limits the effectiveness of many chemotherapies currently used to treat cancer. Drug resistance can occur due to a variety of mechanisms, such as increased drug inactivation, drug efflux from cancer cells, enhanced repair of chemotherapy-induced damage, activation of pro-survival pathways and inactivation of cell death pathways. In this article, we review some of the major mechanisms of drug resistance and discuss how new molecularly-targeted therapies are being increasingly used to overcome these resistance mechanisms.