Both the ROC and the PRC still officially (constitutionally) claim mainland China and the Taiwan Area as part of their respective territories. In reality, the PRC rules only Mainland China and has no control of but claims Taiwan as part of its territory under its "One China Principle".
The strategy of "containment" is best known as a Cold War foreign policy of the United States and its allies to prevent the spread of communism after the end of World War II.
