As the Chinese Civil War ended, the communist party took control of Mainland China and founded the People's Republic of China on October 1, 1949. The Kuomintang (and the Republic of China) retreated to Taiwan. 
Though fighting, including the invasion of several coastal islands by the Communists (with both successes and failures), the bombing of Shanghai and other coastal cities by the Republic of China Air Force, as well as a guerilla campaign waged by remaining Kuomintang forces in southwest China, would continue for the next several years, by the time of the Korean War the lines of control were sharply drawn: the Communist-led People's Republic of China government in Beijing controlled most of mainland China, while the Kuomintang-led Republic of China government, now in Taipei, controlled the island of Taiwan, some surrounding islands, and a number of islands off the coast of Fujian. This stale-mate was enforced with the assistance of the United States government, which, after the start of the Korean War, changed from a policy of abandoning Chiang Kai-shek's Kuomintang regime to the Communists, to protecting Taiwan against an invasion from the mainland, in the First Taiwan Strait Crisis.
Until the 1990s, both governments contended to be the sole legitimate government of China. With the fighting largely over, the major battleground became the diplomatic. Before the 1970s, few foreign governments recognised the People's Republic of China. The first governments to recognise it as the government of China were Soviet bloc countries, members of the non-aligned movement, and the United Kingdom (1950). The catalyst to change came in 1971, when the United Nations General Assembly expelled representatives of the Chiang Kai-shek by refusing to recognise their accreditations as representatives of China. Recognition for the People's Republic of China soon followed from most other governments, including the United States. The Republic of China continued to complete with the People's Republic of China to be recognised as the legitimate government of China.
Since the 1990s, however, a rising movement of for formal recognition of Taiwanese independence has made the political status of Taiwan the dominant issue, replacing the debate about the legitimate government of China. One significant opinion in Taiwan is that the Republic of China and the People's Republic of China are both sovereign, thus forming "two Chinas", or "one China, one Taiwan". The current administration of Republic of China President Chen Shui-bian subscribes to this theory, and accordingly has largely abandoned the campaign for the Republic of China to be recognised as the sole legitimate government of China. Instead, it is campaigning for the Republic of China to join the United Nations as representative of its effective territory - Taiwan and nearby islands - only.