After Jochi and Genghis died, Jochi's lands were divided between Batu and his older brother Orda. Orda's White Horde ruled the lands roughly between the Volga river and Lake Balkhash, while Batu's Golden Horde ruled the lands west of the Volga.
When Batu and his son Sartak died, Batu's brother Berke inherited the Golden Horde. Berke was not inclined to unity with his cousins in the Mongol family, making war on Hulagu Khan, though Berke officially recognized the Khanate of China as his overlord—in theory only. In fact, Berke was an independent ruler by then. Fortunately for Europe, Berke did not share Batu's interest in conquering it.
Batu had at least four children:
Batu's khatun Ukhaa ujin belonged to the Mongol Onggirat clan
In November 1237 Batu Khan sent his envoys to the court of Yuri II of Vladimir and demanded his allegiance. A month later, the hordes besieged Ryazan. After six days of the bloody battle, the city was totally annihilated, and never restored its former glory. Alarmed by the news, Yuri II sent his sons to detain the horde, but these were soundly defeated. Having burnt Kolomna and Moscow, the horde laid siege to Vladimir on February 4, 1238. Three days later the capital of Vladimir-Suzdal was taken and burnt to the ground. The royal family perished in the fire, while the grand prince hastily retreated northward. Crossing the Volga, he mustered a new army, which was totally exterminated by the Mongols on the Sit' River on March 4.
Thereupon Batu Khan divided his army into smaller units, which ransacked fourteen Rus' cities: Rostov, Uglich, Yaroslavl, Kostroma, Kashin, Ksnyatin, Gorodets, Galich, Pereslavl-Zalessky, Yuriev-Polsky, Dmitrov, Volokolamsk, Tver, and Torzhok. The most difficult to take was the small town of Kozelsk, whose boy-prince Titus and inhabitants resisted the Mongols for seven weeks. As the story goes, at the news of Mongol approach, a city of Kitezh was submerged into a lake with all its inhabitants, where it may be seen to this day. The only major cities to escape destruction was Smolensk, who submitted to the Mongols and agreed to pay tribute, and Novgorod with Pskov, which could not be reached by the Mongols on account of considerable distance and winter weather.
In the summer of 1238, Batu Khan devastated the Crimea and pacified Mordovia. In the winter of 1239, he sacked Chernigov and Pereyaslav. After several months of siege, the horde stormed Kyiv in December 1239. Despite fierce resistance of Danylo of Halych, Batu Khan managed to take two principal capitals of his land, Halych and Volodymyr-Volyns'kyi. The Rus' states were left as vassals rather than integrated into the central Asian empire.
Batu Khan then decided to "reach the ultimate sea", where the Mongols could proceed no further. Some modern historians speculate that Batu Khan intended primarily to assure his flanks were safe for the future from possible interference from the Europeans, and partially as a precursor to further conquest. Most believe he intended the conquest of all Europe, as soon as his flanks were safe, and his forces ready.
The Mongols invaded central Europe in three groups. One group conquered Poland, defeating a combined force under Henry the Pious, Duke of Silesia and the Grand Master of the Teutonic Order at Legnica. A second crossed the Carpathians and a third followed the Danube. The armies re-grouped and crushed Hungary in 1241, defeating the army led by Béla IV of Hungary at the Battle of Mohi on April 11. The armies swept the plains of Hungary over the summer and in the spring of 1242 regained impetus and extended their control into Austria and Dalmatia as well as invading Bohemia.
This attack on Europe was planned and carried out by Subutai, under the nominal command of Batu. Subutai achieved perhaps his most lasting fame with his victories there. Having devastated the various Rus principalities, he sent spies into Poland, Hungary, and as far as Austria, in preparation for an attack into the heartland of Europe. Having gotten a clear picture of the European kingdoms, he brilliantly prepared an attack nominally commanded by Batu Khan and two other princes of the blood. Batu Khan, son of Jochi, was the overall leader, but Subutai was the actual commander in the field, and as such was present in both the northern and southern campaigns against Rus. While Kaidu's northern force won the Battle of Legnica and Kadan's army triumphed in Transylvania, Subutai was waiting for them on the Hungarian plain. The newly reunited army then withdrew to the Sajo river where they inflicted the tremendous defeat on King Béla IV at the Battle of Mohi.
Berke did not share Batu's interest in conquering Europe. He was more interested in fighting his cousins, especially Hulagu, whom he loathed for destroying Baghdad. For Berke, a devout Muslim, what Hulagu had done was despicable, and in 1262, when Hulagu prepared to move on Egypt to avenge the defeat of his army (during his absence) at the Battle of Ain Jalut, Berke Khan had Kipchak raiding parties despoil lands considered part of the Il-Khanate. Enraged, Hulagu gathered his armies and marched north, and suffering severe defeat in an attempted invasion north of the Caucasus in 1263, after Berke Khan had lured him north, and away from the Holy Land.
The Kipchak Khanate was known in Rus and Europe as the Golden Horde (Zolotaya Orda) some think because of the Golden colour of the Khan's tent. "Horde" comes from the Mongol word "orda/ordu" or camp. "Golden" is thought to have had a similar meaning to "royal" (Royal Camp). Of all the Khanates, the Golden Horde ruled longest. Long after the fall of the Yuan Dynasty in China, and the fall of Ilkhanate in Middle East, the descendants of Batu Khan continued to rule the Russian steppes.