Who were the Polovtsians?

It occurred to me the other day, while listening (again) to Borodin's "Polovtsian Dances" from his opera Prince Igor, that I did not know who the Polovtsians were or are.

So this being an era when such questions can be answered, I addressed my lack of knowledge on this topic by looking it up.

Turns out that the Polovtsians are more commonly known as Cumans, because that's what the entry explaining who they were -- yes, past tense -- is entitled on Wikipedia.

It starts like this:

"The Cumans, also known as Polovtsians, were a Turkic nomadic people comprising the western branch of the Cuman–Kipchak confederation. After the Mongol invasion (1237), many sought asylum in the Kingdom of Hungary, as many Cumans had settled in Hungary, the Second Bulgarian Empire, and Anatolia before the invasion. 

Related to the Pecheneg, they inhabited a shifting area north of the Black Sea and along the Volga River known as Cumania, where the Cuman–Kipchaks meddled in the politics of the Caucasus and the Khwarezm Empire. The Cumans were fierce and formidable nomadic warriors of the Eurasian steppe who exerted an enduring impact on the medieval Balkans. They were numerous, culturally sophisticated, and militarily powerful."

Here's a picture of two Cuman warriors on horseback, from this article about the Cumani (which is another way to pluralize their name, I guess).