During the wars, the Romulans staged numerous attacks on Earth which had cost the Khanate dearly. Among the casualties were libraries of contemporary history, meaning that the Children of Khan possessed only fragmentary knowledge of the history of the late 20th and 21st centuries. However, the survival of any records of Earth's ancient cultures was credited to Khan's interest in his ancestors.
At one point, Khan seduced and murdered a Romulan commander and was able to escape with her ship's cloaking device. The device was reverse engineered by the Khanate's greatest minds and all Earthfleet vessels were equipped with cloaking devices within several years.
Khan eventually led his people to victory over the Romulans, although they were not conquered as had been the case with the Vulcans, the Tellarites, the Trill, the Betazoids and numerous other races. By 2376, the Romulan Empire was a shadow of its former self due to its long conflict with a race of cyborgs from the Delta Quadrant. (DS9 - Myriad Universes novel: Seeds of Dissent)