The Kuril Islands dispute
Walking around Sapporo, the capital of Hokkaido (the northernmost prefecture in Japan), we saw several times these signs claiming: “Let’s regain Japan’s Northern Territories with the Spirit of the Whole Nation”.
All Kuril Islands were Japanese from 1875 until the San Francisco treaty was signed in 1945, since then the Kuril Islands belong to Russia. Even so, Japan claims the islands as part of its national territory, specially the four islands which are very near Hokkaido (as seen in the sign on the picture). These four islands have a Japanese name and most of its inhabitants belong to the ethnic group Ainu, who speak Japanese (the Ainu language is in danger of extinction)
In this map from Wikipedia you can see how the Japanese control over the Kuril Islands changed over the years.
Some years ago Russia was thinking about giving back some of the islands to Japan, but they eventually backed out.