So, a bit a history I guess. The Kuril Islands are an archipelago that spans south of the Kamchatka Peninsula and north of Hokkaido. In 1855 the Russian Empire and Japan made an agreement that Japan would have the islands south of Urup. In 1875, in exchange for Russia having complete control of Sakhalin, Japan received the rest of the Kuril Islands. However, after the Russo-Japanese war Japan took the southern portion of Sakhalin. However, with the Soviet Union entering the Pacific front of WWII, they retook the rest of Sakhalin, along with all of the Kuril Islands (including those south of Urup).
So, that's where the dispute comes. In 1956, Japan and the Soviet Union made a joint declaration in which the Soviet Union would agree to cede Habomai and Shikotan after the signing of a Peace Treaty. However, the peace treaty never occurred, so Russia continues to have control. A main point of contention is that Japan wants the 1855 boundaries, rather than the Habomai/Shikotan solution.
As for where I stand, the fact of the matter is this: the Soviet Union, and later Russia, have had control over the islands for over 70 years, and Japan has managed to become the world's second largest economy despite that. I think that it is therefore not really necessary for them to continue to claim the islands, and it would make things much simpler for them if they were to just renounce their claims over the Kuril Islands and accept the current de facto situation. It would also help ease tensions with them and Russia and allow progress to be made on that front.
What about you guys?