United Nations General Assembly Resolution 2758

United Nations General Assembly Resolution 2758, adopted on October 25, 1971, replaced the Nationalist Republic of China (ROC) with the Communist People's Republic of China (PRC) as the sole representative of China in the United Nations.

Controversy
The Resolution has been criticized as illegal by the Republic of China government, since expulsion of a member requires the recommendation of the Security Council and can only occur if a nation "has persistently violated the Principles contained in the present Charter," according Article 6. According to the Government Information Office of the Republic of China (Taiwan):
So flawed is this Resolution that only its effective repeal by the General Assembly can provide any hope of expunging the stain on the U.N.’s escutcheon in the international system. Taiwan partially adopted this strategy, and attempted to begin a debate on the repeal of Resolution 2758 during the Fifty-Second General Assembly. Although turned aside in 1997 by the P.R.C.’s energetic diplomatic lobbying, the issue of the R.O.C.’s status at the U.N. will not disappear.
A resolution calling for review of Resolution 2758 noted, "As to its return to the United Nations, the Government has made it clear that it no longer claims to represent all of China, but that it seeks representation only for its 21.8 million people".
However, according to the UN website, no member state has ever been expelled from UN since its inception.
Supporters of ROC admission to the UN argue that the resolution only asserts that the PRC is the legitimate government of China, but makes no mention of the ROC being an illegitimate government, nor of which (if either) is the legitimate ruler of the island of Taiwan, Kinmen, Matsu, and the Pescadores.
Opposers of ROC admission to the UN argue that the PRC is the sole legitimate government of China with Taiwan islands as part of it. The representation of Taiwan islands is already included in Chinese representation in the UN. So the application for the representation of Taiwan in the UN raises the problem of the dual representation of the same region, which is against the generally accepted principle of international laws.
From the viewpoint of the PRC, the ROC is no longer the international legitimate representative government of China since the Resolution 2758, and only the PRC represents the whole sovereignty and territory of China, including Taiwan islands.
Supporters of Taiwan admission to the UN argue that the resolution only asserts that the PRC replaces the ROC as the legitimate representative of China, but makes no mention of the sovereignty issues regarding the island of Taiwan and the Pescadores.
Recently, the US reportedly informed the UN Secretary General Ban Ki-Moon that the resolution only solved the issue of China's UN representation, but did not state that Taiwan is part of China. Japan and Canada also endorsed the US position on this issue. [2] This came after the UN Secretary General arbitrarily rejected Taiwanese application to join the UN under the name "Taiwan" base on his interpretation of the UN Resolution 2758 and his observation that majority of the international community views Taiwan as a part of China.

from wikipedia