They’re known as Takeshima in Japan, Dokdo in Korea, and internationally as the Lincourt Rocks: two ridiculously small volcanic islands located between Japan and South Korea, which were mapped by the French whaling ship Lincourt in 1849 and which both neighbors are claiming ownership of today. The Japanese side of the argument seems to be that they annexed the two uninhabited islands in 1905, which were officially entered into the books as Japanese territory. After World War II the status of the islands was not specifically addressed in the postwar treaties, which is where most of the current problem flows from. There’s plenty of evidence to support each side, for example an 1880 German map showing the rocks as belonging to Japan (hence the world powers of the era considered the islands to be Japanese), a passage in a 1714 historical document in Korea that expressed worry about “Japanese territory” (the Lincourt Rocks) being so close to Korea’s, and the fact that Korea doesn’t seem to have ever named the islands in antiquity or mapped them clearly. On the other side of the argument, there are documents that show that the government of Japan considered the islands as belonging to Korea from the 1870s, and the Korean government did make an official survey of the islands in 1900, five years before Japan’s annexation. The bottom line is that neither side has an iron-clad claim, and each only seemed to start caring about the islands when the other party showed interest, making the whole thing rather like two children fighting over a toy. I predict that South Korea will win the struggle in the end, because a) they have possessed the islands de facto for 50 years now, b) Dokdo/Takeshima are slightly closer to Korea than to Japan, and c) the Koreans are smart enough to make YouTube videos featuring foreigners from around the world holding signs that say “Dokdo belongs to Korea” — if that doesn’t clinch it, nothing will. Even the Korean branch of Dunkin’ Doughnuts got into the fray recently with a line of “Do you know Dokdo?” T-shirts promoting Korea’s claim to the islands. Um, whatevs.
For (way) more information on this topic, Irecommend Occidentalism.org or Dokdo-or-Takeshima, two outstanding resources.