The system of tributary states that existed centered around the various Chinese dynasties for much of East Asia's history is much better understood as a recognition of China's hegemony over the world as they understood it rather than say a "colony" or "puppet state"'of a sort. At least for Korea's example, the system primarily consisted of Koreans officials bringing yearly gifts, or "tributes" (which were substantial) to the imperial court, which was followed by the Chinese court sending goods of their own to Korea as reward, which were oftentimes even more substantial than the original tributes themselves! The rare time when the imperial court did actually invest itself deep into Korea's political affairs was during the Yuan Dynasty, as the Mongols had repeatedly invaded and defeated the Goryeo dynasty in multiple wars prior. The Yuan Dynasty installed its own offices in Korea's capital to keep a careful watch on the kingdom's court affairs and instituted a system of royal marriages in which Korean kings would marry daughters of Mongol emperors, such that the Korean court would be tied to Beijing both politically and by blood kinship. The names of Korean kings during this period were forced to have the prefix "Chung-" (meaning loyalty) to demonstrate their loyalty to the Yuan court, whereas kings from other periods generally usually used what is called a "temple name," which by tradition was only allowed for emperors but was knowingly ignored by various Korean courts. However, even relations between Korea and Yuan wasn't always so bad, and Korean kings at one point were granted titular fief over the "Kingdom of Shenyang" (modern Liaoning). Back to the topic of Korea as a tributary state, it is useful to understand that diplomacy in historical East Asia generally did not consist of nominally equal sovereign states holding embassies in other nations. Unified Chinese dynasties were generally preeminent political, economic, cultural, and military superpowers of that "world," and diplomacy operated with implicit and explicit recognition of China as essentially the "center of the world." It was this recognition of primacy in the pecking order that China demanded from Korea and other tributary states, and apart from this, it had little interest in meddling in their political affairs.