The Republic of China ( Taiwan ) government has controlled Taiwan , Penghu , Kinmen , Matsu and other islands after the rest of mainland China since 1949 .
As a consequence of the World War II and the Chinese Civil War , however , the ROC lost control of mainland China to the Chinese communist party which founded the People 's Republic of China ( PRC ) while gaining and maintaining control of Taiwan , Penghu , Kinmen , Matsu and other islands . The People 's Republic of China ( PRC ) has repeatedly attempted to claim Taiwan as its own territory and refuses to recognize its government and president .