It was Ogodei Khan that ordered the assault on Europe. His father Jenghis was already dead. The Mongols had reached Vienna when they turned back upon hearing of his death. Ogodei had drank himself to death.

Afyer Vienna, the Mongols would have turned South and destroyed the Italian cities that became the cradle of the Renaissance. We might be living with 1913 technology if that had happened.

Tamerlane married a descendant of Jenghis Khan. He never styled himself Khan.

Europe was saved because the Middle East and India were considered more lucrative targets. Europe was poor and underpopulated. It was not worth conquering. However, they did take back European women back to Mongolia as you can see blonde mongols.