There are many disputed territories in the modern world. China claims ownership of Taiwan, Japan claims that South Kuril Islands should belong to it, Argentina claims the Falklands, Gabon claims the island of Corisco, etc. The complete list would be huge.

Usually the pretending country created formal territorial units on the soil it claims. For example, the PRC formally has the “Taiwan Province” and Japan created the counties of Kunashiri, Shikotan, Shibetoro, Shana and Etorofu, which lie on the islands Tokyo has no control of.