Up until 1971, the Republic of China, commonly known as Taiwan, was generally recognized as the "real" China. They were a member of the United Nations and were even a permanent member of the UN Security Council. Then in 1971 they were expelled from the UN and their chair in the Security Council was given to the PRC.

Just how did the world go about to expel a permanent member of the Security Council? And what caused it to happen in 1971, even though US-PRC relations didn't begin to thaw until the following year when Nixon went to meet Mao Zedong?