Double-minute chromosomes play a critical role in tumor cell genetics where they are frequently associated with the overexpression of oncogene products. They have been observed for many years in light microscopic examinations of metaphase chromosomes from tumor cells, but their origin remains unknown and is the subject of considerable speculation. However, molecular details of their structure and organization can now be described in conjunction with the microscopic examinations, to allow an evaluation of the various models that have been developed to explain the genesis of double-minutes. The evidence now favors simple models that invoke chromosome breakage and circularization of very large acentric chromosome fragments, permitting unequal segregation of the genes on the fragment during cell division. If there is selection for overexpression of one of the genes on the fragment, daughter cells with more fragments will grow faster than daughter cells with fewer fragments, and over time the population of cells will come to contain many double-minutes per cell.