After the World War II, nationalist forces relocated themselves to Taiwan where they established the "Republic of China", naming Taipei as a "temporary capital" - similair to North Korea's proclaiming of Pyongyang only a "temporary administrative center".
From Taipei, they operate and seek control of whole of the China as we know today, asserting their legitimacy as the rightful succesors of the Qing Empire.
Source: https://www.facebook.com/geopoliticalstudiesinPrague/