The helical nature of the double helix causes a topological problem for its replication. Watson and Crick were well aware of this potential problem, and in 1953 they stated: "Since the two chains in our model are intertwined, it is essential for them to untwist if they are to separate... Although it is difficult at the moment to see how these processes occur without everything getting tangled, we do not feel that this objection will be insuperable." We now know that this problem is solved by the DNA topoisomerases, which were first reported in 1971 by James Wang, with the discovery of bacterial topoisomerase I. Over the past ~40 years these enzymes have been found in all organisms (prokaryotes, eukaryotes, viruses and archaea) and to perform roles that are vital for survival, supporting replication, transcription and other processes where topological problems in DNA need to be resolved. The enzymes are ‘marvelous molecular machines’ catalyzing the seemingly magical task of passing one piece of DNA through another to catalyze changes in DNA topology. Some of the enzymes are molecular motors having the ability to transduce the free energy of ATP hydrolysis into torsional stress in DNA (supercoiling). Although the outline of their mechanisms has been established, a great deal is unknown and emerging technologies, such as single-molecule methods, need to be applied to gain a deeper understanding of these enzymes and their roles in cellular processes. Topoisomerases have also become key drug targets both for anti-bacterial and anti-cancer chemotherapy. This is due to their essential nature and because of their mechanism of action, which involves transient DNA cleavage that, if disrupted, can lead to highly cytotoxic events. Study of these enzymes in the context of myriad cellular processes is of key importance in research leading to the development of new chemotherapeutic agents.