Although cancer diagnoses during pregnancy are rare, they have been increasing with the rise in maternal age and are now a topic of international concern. In some cases, the administration of chemotherapy is unavoidable, though there is a relative paucity of evidence regarding the administration of anticancer drugs during pregnancy. As more cases have gradually accumulated and further research has been conducted, we are beginning to elucidate the appropriate timing for the administration of chemotherapy, the regimens that can be administered with relative safety, various drug options and the effects of these drugs on both the mother and fetus. However, new challenges have arisen, such as the effects of novel anticancer drugs and the desire to bear children during chemotherapy. In this review, we outline the effects of administering cytotoxic anticancer drugs and molecular targeted drugs to pregnant women on both the mother and fetus, as well as the issues regarding patients who desire to bear children while being treated with anticancer drugs.