This is a summary of Cuman history based on easily found sources. I tried to compare sources to detect errors of fact, but as most of the information has not been peer reviewed, it may contain some errors.  Any that exist I hope to correct with time. 
 
HISTORY OF THE KUMANS
Revised 2/25/2006
Copyright © 2006 All Rights Reserved

The Cumans or Kumans are described as a nomadic Turkic people whom the Russians called Polovtsi (the word in old Slavonic for “pale yellowish”). They are identified with the Western branch of the Kipchaks, a name given to the Kumans by the Arabs. Interestingly enough the Kipchaks are mentioned in Chinese manuscripts from the 300s BC and Arab writings from 820s AD and 950s AD. From various documents in which these tribes are mentioned (including the Kimaks who ruled over several tribes including Kipchaks) it is believed they first were found in what is today western Kazakhstan in the steppes by the Aral Sea. (That area also included the Pechenegs who moved west earlier, the Bashkir (who can still be found there) and the Oguz. According to Dmitriy V. Ryaboy, it was political circumstances that caused the Kumans to separate from the Kimaks and moved west. By the 11th Century they had settled in the steppes near and between the Volga, Don and Donets Rivers. Maps of Eurasia for 1000 A.D. place them there.  

According to Ryaboy, the Kumans were divided into hordes, each led by a khan. Horde society was divided into smaller units that traveled together. These units had several social classes: leaders, warriors, freemen and slaves. A Khan’s name usually ended with -kan, or -niak. Names of leaders of the smaller units typically had names ending typically with -opa, -oba or -epa.

According to writings by the Arabs the Kumans/Kipchaks were pagans who practiced astrology and stone magic. By the 900s a small few became followers of Islam.  By 1200 A.D. they had pushed west and south to extend all the way across the top of the Black Sea to the Danube River. Today those areas are now called Southern Ukraine, Moldova, Wallachia and Transylvania. They waged war against the Byzantines, the Hungarians and the Kievan Rus. The Kumans survived the initial Mongol incursions of the 1230s A.D. only to ultimately fall to them  in 1242. They did however survive to establish the principality of Wallachia in present day Romania on the north side of the Danube river. Wallachia’s earliest rulers were Kumani. The Kumans had joined in the Vlach-Bulgar Rebellion of 1185/1186 and must have become leaders in the society at that time. By the early 1300s, Basarab I, son of Tihomir, the Kumani warlord of Wallachia obtained independence for the region from Hungary.
 
The Russians preserved stories of their struggles with the Kumans in several epic tales:   The Battle of the Stugna River, The Battle of the Kalka River, and the Tale of Igor'’s Campaign.  A timeline of the Russian-Polovtsy Wars was printed in Rodina (1997), 3-4. A translation is provided by Norman J. Finkelshteyn at redkananate.org.

With the Mongol incursion of 1242, many Kumans fled West and North, into the mountainous regions, into Hungary, Bulgaria and elsewhere.  This was during the reign of Ogodei (1229-41) Ghengis' sucessor and third son. These campaigns swept across the steppes to Russian Moscow and as far north as Yaroslavl' in 1238, then down into the Caucasus. By 1240, the Mongols travelled up and over to Kiev, Krakow and Galich in Galicia, then down into Hungary and Serbia.  In 1242 they swept across Bulgaria to engage the Kumans in the region stretching from the Danube to the Dnieper Rivers.  Those Kumans that remained in the Volga region and survived the Mongol incursion ultimately joined the khanate of the Golden Horde and eventually became Muslim. The Kumans in the West became Christian and an area that included Romania and Moldova held the name of Diocese of the Kumans until 1523. 
 
According to Wikipedia, Kumani words appear in place names in the Balkans and elsewhere: in the Macedonian city of Kumanovo, the Moldavian city of Comanesti, and in Dobruja (Black Sea coastal area south of the Danube) at the city of Comana. Several counties of Hungary include the root “kun” (which Wikipedia asserts is the Cuman name root) in their names such as Bacs-Kiskun and Jasz-Nagykun-Szolnok and in town names such as Kiskunhalas and Kiskunszentmiklos. There is a town in the Polish Carpathians named Komanzca (just north of the old Lupkow Pass) and it is believed that the origin of the name is Kumani.

The Kumans spoke a Turkic language most similar to the modern Crimean Tartar language. The language was codified in medieval era texts such as the Codex Cumanicus, which is believed to be a linguistic manual for the use of Catholic missionaries to the Kipchaks.  

Marco Polo also mentions the Kumans in his writings. He describes a region that Alexander the Great had tried to conquer without success.  Marco Polo stated that historical accounts say that the Tartars lived there, but according to him the region was inhabited by the Kumans “with a mixture of other nations.” One of the tales he relayed was that their kings in ancient times were known because of the mark present from birth, of an eagle on the right shoulder  Alexander had tried to gain access to this region through a narrow pass that extends for four miles along the Caspian Sea and the Caucasus mountains. Because the pass could easily be defended by a small number of warriors he was readily defeated and unable to advance. As a result, Alexander is said to have built a fortress and a gate of iron to "keep out" those Northern Warriors. Derbent, Russia is the town in the area that most closely fits the description provided. By Marco Polo's time the people were described as Eastern Christians, “bold sailors, expert archers and fair combatants in battle.” Their province had many towns and castles; they produced silk and cloth of silk interwoven with gold.  

There are probably many more historical records on the Kumans in the East, but we English speakers will have to wait for translations. Already with the fall of the Iron Curtain so much more has become known in the West than ever before. Roman Zakharii of Berezhany has translated from the Russian portions of “"Sketches on the History of Galician – Volhynian Rus"” by V.T. Pashuto that discusses the relations between Galicia and the various Hordes of the 13th century. His translation mentions that in the 1280s, NogayKan provided Leo of Galicia military assistance including troops under the command of the warlord Konchak who was probably of Cuman origin. Interestingly enough a Ukrainian map of the Duchy of Galicia, shows it extending all the way from the source waters of the Pripet River down to the mouth of the Dniester and Prut rivers at the Black Sea. Unfortunately there is no date on the map.  

Erika Bogacsi-Szabo did a study of mitochondrial DNA from excavated early Kuman populations and compared them with modern Hungarians from a variety of rural locations in Hungary.  She found that "while still possessing a Central Asian steppe culture, the Cumanians received a large admixture of maternal genes from more westerly populations before arriving in Hungary. A similar dilution of genetic, but not cultural, factors may have accompanied the settlement of other Asian nomads in Europe. "

Sources:

www.answers.com

Bogacsi-Szabo, Erika "Mitochondrial DNA of Ancient Cumanians: Culturally Asian Steppe Nomadic Immigrants with Substantially More Western Eurasian Mitochondrial DNA Lineages" Human Biology - Vol. 77(5): 639-66(October 2005).  
 
Columbia Encyclopedia, 6th Edition 2005  
DK Atlas of World History, Black J. gen. editor, Dorling Kindersley Publishing Inc. (New York 2000) 
 
Ryaboy, Dmitriy V., The origins of the Polovtsy, www.redkaganate.org/tribelist/polovtsi.shtml  

Sketches on the History of Galician-Volhynian Rus by V.T. Pashuto (1950) Translation by Roman Zakharii in 2002, www.personal.ceu.hu/students/97/Roman_Zakharii/gal.htm  

The Travels of Marco Polo, by Marco Polo, revised from Marsden’'s Translation. Komroff, Manuel, ed.  

Wikipedia, online at wikipedia.com