This article is from the Tibet FAQ, by Peter Kauffner Peter.Kauffner@bearsden.org and Nima Dorje email@example.com.
Here is how the Chinese Communist magazine _Beijing Review_ explains it:
From ancient times, the Mongolians had been one of China's
nationalities. In the 13th century, their power expanded rapidly.
Genghis Khan united the tribes under a centralized Khanate in 1206.
The outcome was a unified country [China] and the formation of the
Yuan Dynasty in 1271.
In the process, the Mongol Khanates peacefully incorporated Tibet
in 1247 after defeating the Western Xia  and the Jin .
With a unified China, the Yuan Dynasty contributed greatly to the
political, economic and cultural development of the nation's various
nationalities -- in strict contrast to the feuding that had gone on
since the late years of the Tang Dynasty (618-907). To argue that the
Mongolians' campaign to unify China was fundamentally the imposition
of rule by a foreign power is wrong because it misses the basic point
of Chinese history that China is a multi-national country. Whether it
was the Mongolians, the Manchus (who founded the Qing Dynasty [1644-
1912], or any other peoples, it has always been a case of one Chinese
nationality replacing another. It is completely out of the question to
claim that the Mongolians or the Manchus were outsiders who conquered
The Dalai Lama's view is as follows:
During the Vth Dalai Lama's time [1617-1682], I think it was quite
evident the we were a separate sovereign nation with no problems. The
VIth Dalai Lama [1683-1706] was spiritually pre-eminent, but
politically, he was weak and disinterested. He could not follow the
Vth Dalai Lama's path. This was a great failure. So, then the Chinese
influence increased. During this time, the Tibetans showed quite a
deal of respect to the Chinese. But even during these times, the
Tibetans never regarded Tibet as a part of China. All the documents
were very clear that China, Mongolia and Tibet were all separate
countries. Because the Chinese emperor was powerful and influential,
the small nations accepted the Chinese power or influence. You cannot
use the previous invasion as evidence that Tibet belongs to China. In
the Tibetan mind, regardless of who was in power, whether it was the
Manchus, the Mongols or the Chinese, the east of Tibet was simply
referred to as China. In the Tibetan mind, India and China were
treated the same; two separate countries. [Gyatso89]