Espn has declared Taiwan and islands in the South China Sea as part of China. 
The Republic of China (Taiwan) is obviously an independent country. It has its own government, military, police, laws, economic sysyem, currency etc. It also still uses Traditional Chinese writing while the communists on the mainland switched to Simplified Chinese to prevent people reading anything from before the communist takeover.
The communists vowed to take it by force by 2020, but if they were able to they would have already. They can't because the country is well armed and like a huge aircraft carrier.
The communists can't stand its existence because it shows that a democratic, free-market and successful China can exist and does. Also, it still claims to be the legitimate government of all of China.