Korea has long history with steppe nomads and its northern regions (Manchuria), and various Korean kingdoms had to deal with invasions, wars, and border conflicts all the same as China. Often when we hear of Korea's ancient and medieval history we think of it as very peaceful, but the northern frontier regions (using the modern borders of Korean peninsula) was anything but. Realistically, this is going to be more a explanation on the history of the Manchurian region than on the nomads alone as from the Korean perspective, the nomads and China were somewhat interchangeable.

First, the Manchurian region was a hotly contested one between Korea, China, and steppe nomads. The modern delineation between China and the Korean peninsula uses the Duman (Tumen) and Amnok (Yalu) rivers as its natural borders but this was something Korea had to fight and win over gradually against both China and the nomads.

It's difficult to figure where exactly to start since precluding the ancient ancient history would mean a lot of interesting conflicts are missed, but I guess to best summarize we can go with Manchuria was occupied by the successive Korean kingdoms: Gojoseon -> Wiman Joseon (a Sino-Korean mix) -> Han commanderies (China) -> Buyeo -> Goguryeo -> Balhae (Korean-Jurcheon/steppe nomads mix I believe). Keep in mind there are a lot of caveats that are missed here; what we say as Korea or China in the modern sense is not something that exists. It is retroactively applied to make things easier to understand but the truth is there is a lot of intermingling between Chinese, Koreans, and the nomads. However, East Asian historiography still has major problems with nationalism which does make it difficult to objectively understand this period. I can explain more if you'd like to know more, but I'd like to just get into the main points.

The northern Korean kingdoms in Manchuria (the last one being Balhae) eventually collapsed from nomadic invasions by the Khitan in the 10th century as unrest spread all over East Asia. Chinese Tang dynasty collapsed, the southern Silla kingdom in Korea collapsed as well which led to the rise of a unified Korean dynasty, Goryeo. Khitans claimed themselves as the Great Liao dynasty and occupied Manchuria and northern China while eventually the Song dynasty claimed the mandate of heaven in China as well. In this period, the interaction between Korea and China was greatly weakened because the Khitans to the north began invading Goryeo Korea because Goryeo were sending their envoys to the Song as recognition of their claim to the mandate instead of sending their envoys to the Khitan. Goryeo was also itching for war in some respects because one of the dynasty's goals was to recover Manchuria from the "barbarians" that were occupying "Korean" lands.

The following Goryeo-Khitan war was eventually settled in the early 11th century. Goryeo began to send their envoys to the Khitan after as well, in a dual recognition of both Song and Liao, while the Khitan ceded territories south of the Amnok river, a change in territory that continues to persist to today.

However, the Khitan Liao collapsed to the Mongol Yuan dynasty in the 13th century and Goryeo also capitulated as well. This is probably the more well-known part of interaction between the nomadic empires to the north of Korea and Korea itself since Mongols famously conquered, well, everything but Japan and Vietnam.

Under the Yuan dynasty, Goryeo royalty were often sent to China as hostages and were forced to intermarry with the Yuan Mongols. Eventually as the Yuan weakened Goryeo under King Gongmin implemented anti-Mongol policies and removed pro-Mongol officials and reclaimed their independence. The Yuan dynasty itself collapsed to the Ming dynasty after the Red Turban rebellion. This rebellion spilled into Korea itself as the rebels in Liaodong peninsula were looking for supplies, which Goryeo managed to beat back. Additionally, in this moment of weakness in China, the Goryeo court authorized an invasion of Manchuria as a part of a campaign to recover lost Korean territories in the north. However, the general chosen to lead to attack went up until the river border between Manchuria and Korea and decided to turn back and rebel against Goryeo. The newly established Joseon dynasty succeeding Goryeo was heavily pro-Ming.

During Joseon period, Korea was in constant conflict against the Jurcheon tribes (that were nominal vassals to the Ming) that were occupying Manchuria. Gradually, the Joseon kingdom expanded to the Duman river, establishing the modern Korean peninsula borders we know today.

In the 17th century however, the Jurcheon tribes were united under a powerful warlord named Nurhaci and the Ming was invaded and overthrown eventually by Nurhaci's son who established the Qing dynasty. Qing invaded and capitulated Korea and forced them to enter a tributary relation. And the story sort of just ends here. After the Jurcheons (also called Manchu) conquered China and forced Korea into a tributary relationship, Korea entered a long period of peace until the West came knocking because its sole land border was shared with the Chinese Empire and the Qing recognized the two rivers as the natural border between China and Korea.

Hope this helps. Ended up much longer than I thought.