After Japan’s defeat in World War 2, Russia invaded the Kuril Islands (red cross on the map). That’s the reason the two countries never singed the end of the war. After the nuclear accident of Fukushima in 2011, Japan became the largest importer of expensive liquefied natural gas (LNG). Note that the Japanese economy is quite “thirsty”, since it is the third largest economy after the US and China.
The Japanese and the Russians are discussing the possibility of jointly construction an undersea pipeline, in order for Japan to by cheaper Russian gas. In that case the Russians would be willing to return to Japan some of the Kuril Islands.
Besides the obvious benefits for the Japanese economy, the Japanese would also see the Russians being neutral in the Japanese-Chinese struggle over the Senkaku Islands. There would be of course the problem that the Japanese would find it harder to support her main ally i.e. the US, in the American-Russian confrontations.
“Japanese Lawmakers to Lobby Abe for Russian Gas Pipeline”, May 2014
“Japan’s Abe to try and resolve World War II row with Russia”, January 2016