The "history war" in Northeast Asia
The big dog in this fight is the legacy of the kingdom of Koguryo, as the Koreans refer to it, or Gaogouli, as the Chinese call it. (In Korea, another variant spelling is "Goguryeo." I will more or less randomly choose between all three spellings to avoid accusations of ideological bias -- in the shark-infested historical waters of Asia, dread partisanship can be determined by the choice of a K over a C.)
The Kingdom of Koguryo existed from the first century B.C. to 668 A.D. At its height, under the Emperor Gwanggaeto the Great, it controlled a significant section of Northeast Asia, including territory that is now part of South Korea, North Korea and China. From a Korean historical vantage point it has long been considered one of the Three Kingdoms of Korea, a major wellspring of Korean civilization and culture.
But according to China, Gaogouli is historically Chinese, an assertion that outrages Korea. Dating back at least as far as 1980, but picking up steam with the inauguration of China's "Northeast Project," Chinese historians have been pumping out research papers that claim that Gaogouli should be considered an integral part of the historical concept of "China."
Korean nationalists scoff at such assertions, and make counter accusations that describe Chinese historical revisionism as motivated by claims on Korean territory -- such as Mount Baekdu. Those Western historians who have explored the topic make a pretty convincing case that the Chinese interpretation does not hold water; that it is a clear political attempt to provide legitimacy for current Chinese borders by pretending that everything currently part of China has always been part of China.