In the 13th century, Mongol hordes invaded most of the known world and Genghis Khan's nobles had strong legacies to rule in China, Iran and Central Asia in the the following centuries. What about the Mongol soldiers and common people in the areas? Were they assimilated or dissolved in any sense or do the descendants of Mongols still live in areas other than Mongol proper?
Wikipedia provides an excellent answer on the Descendants of Genghis Khan.
Some of the main points:
Another important consideration is that Genghis's descendants intermarried frequently. For instance, the Jochids took wives from the Ilkhan dynasty of Persia, whose progenitor was Hulagu Khan. As a consequence, it is likely that many Jochids had other sons of Genghis Khan among their maternal ancestors.
Among the Asian dynasties descended from Genghis Khan were the Yuan Dynasty of China, the Ilkhanids of Persia, the Jochids of the Golden Horde, the Shaybanids of Siberia, and the Astrakhanids of Central Asia.
The ruling Wang Clan of the Korean Goryeo Dynasty became descendants of the Genghisids through the marriage between King Chungnyeol and a daughter of Kublai Khan. All subsequent rulers of Korea for next 80 years, through King Gongmin, were thus descended from Genghis Khan.
After the Mongol invasion of Russia, the Rurikid rulers of Russian principalities were eager to obtain political advantages for themselves and their countries by marrying into the House of Genghis.
...Hence, it is not surprising to note that from Nurhaci to the Shunzhi Emperor, all the empresses and major concubines were Mongols.
It is also worth noting The Ian Ashworth Effect also mentioned in the link above and in this SE Skeptics discussion:
It has been claimed and researched (link to paper) that:
8% of all Asian men and thus 0.5% of all men would be descendant of Genghis Khan.
The conclusion from Skeptics was that the research stacked up:
It appears to have a robust result, that it seems reasonably to provisionally accept unless counter evidence is produced.
The vast majority of Genghis Khan's Mongols either were driven back to Mongolia or were absorbed into the general population of China. Some modern-day Chinese do retain their Mongol heritage as evidenced in the following linguistic map of Mongol Languages:
Some of the Mongol populations include: Bonan, Mongour, Dongxiang, Yugur, Sogwo Arig, Sichuan Mongols, Yunnan Mongols. Thanks to Dagvadorj for correcting me and pointing that out.
Genghis Khan's empire had at least four main parts: (modern) Russia, the Middle East (mainlhy Persia), Central Asia (Kazakhstan), and China-Mongolia.
The soldiers who occupied the first three parts (mostly) intermarried with local women. In China-Mongolia (under Kublai Khan), many Mongolians intermarried with Chinese. Only a few Mongolians (between modern Mongolia and Lake Baikal) remained relatively "pure," which is why there are so few of them today. The genes of the others ended up elsewhere.