For most part of pre-modern China, China was constantly being invaded by border tribes that were partially "sinicized" (adopted some parts of Chinese culture).

Prior to unification around 230 BC, several Chinese Kingdoms were considered to be mixed barbarians. The massive Chu kingdom in the South, for example, were people who were least sinicized among all of the Chinese Kingdoms at the time.

The Kingdom of Qin that conquered all of China, was originally a Kingdom of mostly barbarian Qiang people who were horsemen on the Western frontier of China, who became sinicized over time. (the descendants of Qiang people still live in Western China today).

During the Northern Southern Dynasties era, China was successively invaded by 2 Kingdoms West of China, the Di and Qi people, who were sinicized "proto-Tibetan" tribes. Each time, Di and Qi managed to conquer most of Northern China, but were repelled by Southern China.

The Di and Qi people were not related to what we know as the modern Tibetans, who were related to Mongols.

Then during Sui Dynasty, the Sui rulers (the Yang clan) rose up originally as part Turkish warlords, in West of China.

Their successors of the Tang Dynasty, the Li clan were also part Turkish Warlords West of China.

During the Tang Dynasty, the Tibetan military empire invaded China and briefly occupied Chinese capital, taking advantage of a Chinese internal rebellion by an usurper, and installed their puppet Chinese Emperor.

*So, the general historical pattern in China was that various Barbarian tribes/kingdoms/warlords would rise up and try to invade/unify China. (Often time, such tribes rose up in the West of China. This is the reason why the Chinese capital for most part of Chinese history was near Xian, meaning literally "Western Peace", a city located closer to the Western frontier of China).

The Mongols penetrated quite deep into Chinese territory as you have to remember they actually ruled over all China and overthrowed the Sung dynasty at that time, though not for long. The Manchus were the same, they completely demolished the Ming dynasty and set up the Ching (or Manchu China) dynasty. What's different between the Ching and the Mongols were that the Mongol empire quickly shattered but the Qing actually ruled for a few hundred years. As for foreign invasions, you will have to define what is invading. I could tell of the semi-colonisation by the Western Powers at the late Qing period, which was marked by the Opium Wars. Another famous invasion was the Japanese invasion in WW2, which most Chinese still haven't forgotten and still stirs up problems in foreign relations between China and Japan. Hope this helps.