Most famous ruler was Genghis Khan and then his son Kublai Khan.
No specific capital, After Genghis Khan died they divided empire into 4 different states with 4 leaders and 1 Great Khan who ruled over all of them
There culture was very war centered. Historians say they were the most effective military force in history until the modern age. People would surrender as they got word of the Mongols coming. Although they conquered brutally, they ruled with peace and accepted all religions.
They did not have many architectural achievements as they believed in moving around rather then staying in one place. Although they did not have many architectural achievements they mad great advances in warfare. A great non physical achievement is the fact that there are 16 million direct descendants of Genghis Khan!
The Mongols are often talked about in relation to how Brutal and bloodthirsty they were. Although this is true there are many things not talked about. Like how the mongols were responsible for the rise in trade in the era. They emphasized trade because they could tax it and made the roads safe for trade. The mongols also were very religiously tolerant and allowed all religions.
Although they were foreign to Chinese people the mongols tried to relate to them as much as they can. The adapted many Chinese aspects of life and even gave there dynasty a Chinese name, Yuan. The Yuan Dynasty was after the Song and constantly feared rebellion from song supporters in the south. Some Chinese began to accept them near the end.