The official name of Taiwan is the Republic of China. That government used to control all of China. Then there was a communist revolution and the ROC governme

The official name of Taiwan is the Republic of China. That government used to control all of China. Then there was a communist revolution and the ROC government fled to Taiwan, still claiming to be the rightful government of China, merely having been forced to make a tactical retreat. This is still the official position of the ROC government, even if no one really believes that the ROC will one day return and reconquer the mainland. Now to be fair, Taiwan probably would have simply declared independence and given up on the mainland but for fear that this would lead to a PRC invasion. The government even really acts officially as if it is the government of all of China sometimes, such as its support of the PRC in certain maritime claims. The ROC claims certain islands are "part of China" even though they would fall under the physical control of the PRC and thus don't really concern Taiwan.