DNA topoisomerases are essential nuclear enzymes that are involved in DNA replication. Clinically useful antitumor drugs such as doxorubicin, daunorubicin (anthracyclines), etoposide, teniposide (epipodophyllotoxins), and amsacrine (an aminoacridine) interfere with the function of topoisomerase II and camptothecin and its analogs inhibit topoisomerase I. Some mammalian tumor cells that express resistance to drugs that interfere with topoisomerase I or topoisomerase II have alterations in their respective topoisomerases. In this paper, we review the functions of the topoisomerases, discuss aspects of their cellular regulation, ask how interference with topoisomerase function can lead to tumor cell death, discuss the biochemical features of tumor cells that are resistant to these anti-topoisomerase drugs, and, in the context of drug resistance, we raise questions about how these drugs exert their cytotoxicity.