The seminal papers by Watson and Crick in 1953 on the structure and function of DNA clearly enunciated the challenge their model presented of how the intertwined strands of DNA are unwound and separated for replication to occur. We first give a historical overview of the major discoveries in the past 50 years that address this challenge. We then describe in more detail the cellular mechanisms responsible for the unlinking of DNA. No single strategy on its own accounts for the complete unlinking of chromosomes required for DNA segregation to proceed. Rather, it is the combined effects of topoisomerase action, chromosome organization and DNA-condensing proteins that allow the successful partitioning of chromosomes into dividing cells. Finally, we propose a model of chromosome structure, consistent with recent findings, that explains how the problem of unlinking is alleviated by the division of chromosomal DNA into manageably sized domains.