At the very beginning of the Mongol Empire in 1208, Genghis Khan defeated the Naimans and captured an Uyghur scribe, Tatar-Tonga, who then adapted the Uyghur alphabet — a descendant of the Syriac alphabet, via Sogdian — to write Mongol. With only minor modification, it is used in Inner Mongolia to this day. Its most salient feature is its vertical direction; it is the only vertical script that is written from left to right. (All other vertical writing systems are written right to left.) This is because the Uighurs rotated their script 90 degrees counterclockwise to emulate the Chinese writing system.
The traditional Mongolian alphabet is not a perfect fit for the Mongolian language, and it would be impractical to extend it to a language with a very different phonology like Chinese. Therefore, during the Yuan Dynasty (ca. 1269), Kublai Khan asked a Tibetan monk, Phagspa, to design a new alphabet for use by the whole empire. Phagspa extended his native Tibetan script to encompass Mongolian and Chinese; the result was known by several descriptive names, such as the Mongolian seal script, but today is known as the Phagspa alphabet. This script did not receive wide acceptance and fell into disuse with the collapse of the Yuan dynasty in 1368. After this it was mainly used as a phonetic gloss for Mongolians learning Chinese characters. However, scholars such as Gari Ledyard believe that in the meantime it was the source of the Korean Hangul alphabet.
Thus, within two generations, the latter around the time of the sojourn of the Polos (Marco, his father, and his uncle) at Kublai's court, we had two alphabets imported for use in writing one language. The Tibetan script gave rise to the Phagspa script, which in one hypothesized pedigree was the precursor to Hangul. Small world!
I've also been reading a little about Chinese history, particularly the Qing Dynasty, the Chinese Civil War, and the Soong Sisters.