As you can see, Korea is a peninsula between China and Japan. This made it easy for the two countries to effect its culture. Similar to Japan, the mountainous terrain of Korea made it hard to farm. Most lived in the west, the flatter area. These people were nomads, and formed clans as their culture developed. China would seize part of Korea, and so they adopted some of the Confucian ideas, Chinese writings, political institutions, and agriculture methods. Eventually China would lose Korea to the Silla, but they would take all of the country under their rule. However, the Silla were allies to China and would pay tribute. They had adopted much of China's culture, and so they ruled Korea as China would.
The Silla would lose control when a rebellion broke out. The Koryo dynasty was founded, the namesake of Korea itself. While they kept some of the Chinese customs, Koryo rulers worked to keep Korea's culture separate. Their civil service exam could only be taken by nobles, for instance. This would mean that nobles and common fold were separated, however.
Korean culture thrived. A new type of pottery would outshine the porcelain so beloved by the Chinese. This is called celadon.
As you can see, it is quite beautiful. Korea would also use Chinese printing methods in order to print Buddhist texts. They would even improve it, inventing the metal moving type.
Korea's period of one-upping China would sadly end when the Mongols arrived. They would demand huge tribute from Korean rulers, and force many people into slavery. They made men serve in their army, and stole all the artisans of Korea for themselves. However, after a weak point in the Yuan dynasty, Korea would come back strong in rebellion. A new dynasty would rise, allowing Korea to think of more ways to one-up China. This dynasty was called the Joseon Dynasty. How did they beat China this time? On the run way, with these fine threads.