© 2017, Springer-Verlag Berlin Heidelberg. To resolve the topological problems that threaten the function and structural integrity of nuclear and mitochondrial genomes and RNA molecules, human cells encode six different DNA topoisomerases including type IB enzymes (TOP1 and TOP1mt), type IIA enzymes (TOP2α and TOP2β) and type IA enzymes (TOP3α and TOP3β). DNA entanglements and the supercoiling of DNA molecules are regulated by topoisomerases through the introduction of transient enzyme-linked DNA breaks. The covalent topoisomerase–DNA complexes are the cellular targets of a diverse group of cancer chemotherapeutics, which reversibly stabilize these reaction intermediates. Here we review the structure–function and catalytic mechanisms of each family of eukaryotic DNA topoisomerases and the topoisomerase-targeting agents currently approved for patient therapy or in clinical trials, and highlight novel developments and challenges in the clinical development of these agents.