History
China became a republic under the leadership of Sun Yat Sen and later Chiang Kai Shek. After the civil war with Moa Zedong-led Communists, Chiang Kai Shek’s Nationalists retreated to Taiwan from Mainland China in 1949. Ever since, Communist China has maintained that it is the legitimate government of Taiwan and that Taiwan is a renegade state.
Because of the political pressure exerted from China, and lack of a seat at the United Nations, few countries officially recognize Taiwan as an independent country – hence you’ll not find embassies in Taiwan, but “trade offices” performing the same functions.
Regardless of all the saber-rattling, if China poses any genuine threat to Taiwan it is balanced by the fact that the United States stands firmly behind Taiwan on the grounds of democracy and even more so because of the massive trade between the parties. The situation has in fact been fairly stable now for almost 50 years. If there were to be a change, it would almost certainly be through diplomatic channels.