From the European perspective, the Mongols were just another in a long line of horseback nomads who attacked from the east, raided and plundered, then disappeared back to the steppes, like the Huns seven centuries earlier. Their attacks on eastern Europe were terrifying, unpredictable, and nearly impossible to defeat, but the Mongols were still just a barbarian tribe, of no real political importance to the nobles in western Europe. However, from a more worldly perspective, the Mongols ruled the largest empire ever seen, stretching from the East China Sea to Poland and Hungary, from Siberia to Persia and Southeast Asia. The Mongols might not have had much in the way of traditional civilization, but they had a civilized approach to trade, and by the end of the 13th century, trade routes flourished from China to the Middle East and Europe; it was possibly the first time that China and Persia had knowledge of each other.
The Mongol empire began in 1206, when a successful warrior and leader named Timuchin was elected supreme ruler, or Genghis Khan, of the Mongol tribes. Genghis Khan was able to unite the varied nomadic tribes into a coherent army, which he then used to expand Mongol territory. In 1211, he attacked the Chin dynasty, the rulers of northern China; while he was beleaguering China, he sent armies to attack Persia, taking Samarkand in 1220, then turned his attention to Russia. Mongols had conquered most of Russia by 1240, then moved east to Europe and took Poland and Hungary by 1242. Further attacks on Europe were prevented only by the death of the Khan and dynastic struggles which called the armies back to Mongolia. By the middle of the thirteenth century, Mongols controlled Korea, northen China, Persia, and Russia, in addition to the steppes of interior Asia; by 1280, Kublai Khan had united all of China and founded the Yuan dynasty, which lasted for 100 years.
It wasn't until 1260 that the Mongols suffered their first major defeat, at the hands of the Mamluks of Egypt, who turned them back in the Middle East; in the east, their major set-back was their inability to attack Japan successfully, in large part because they were horsemen rather than sailors. The Mongols maintained the peace in their empire vigorously, allowing no civil wars, and the Pax Mongolia may be the largest war-free zone ever created; it lasted until 1294, and, in parts, for several more centuries. It was almost certainly the most tolerant of various religions, much more so than Europe was at the time; at various times, the Mongols were animist, Buddhist, Muslim, and Christian, and subject peoples were allowed to follow their own religions as long as they did so peacefully. In terms of religion, trade, and keeping the peace, the barbarian Mongol empire was much more civilized than medieval Europe.