Short answers, pulled from the story.
The Pechenegs were a semi-nomadic Turkic people who originated in Central Asia, with their homeland located between the Aral Sea and the middle course of the Syr Darya. Pushed westward by an alliance of Oghuz, Karluks, and Kimaks before 850, they eventually settled across the steppes of southeast Europe and the Crimean Peninsula by the 9th and 10th centuries.
At the Battle of Levounion in 1091, the Pechenegs were annihilated as an independent force by a combined Byzantine and Cuman army under Emperor Alexios I Komnenos. The survivors were settled by Alexios I in the district of Moglena, in what is today Macedonia, and formed into a military unit called the tagma of the Moglena Pechenegs.
The Pechenegs, allied with Tsar Simeon I of Bulgaria, drove the Magyars out of the Pontic steppes at the Battle of Southern Buh, forcing them to leave the region called Etelkoz permanently. The Magyars then settled in Pannonia, where they later founded the Hungarian state.
The Pechenegs as a group were last mentioned in 1168, when chronicles recorded them as members of a Turkic confederation known as the Chorni Klobuky, or Black Hats. In Hungary, the administrative title Comes Bissenorum, Count of the Pechenegs, lasted for at least another 200 years after that.
The Pechenegs spoke the Pecheneg language, a Turkic tongue closely related to the Cuman and Oghuz idioms, according to the 11th-century linguist Mahmud al-Kashgari. The Pechenegs are thought to have belonged to the Oghuz branch of the Turkic family, though the language is poorly documented and died out centuries ago.
In 972, Pecheneg forces ambushed and killed the Kievan prince Sviatoslav I. The Primary Chronicle records that Pecheneg Khan Kurya then had a chalice made from Sviatoslav's skull, following the custom of steppe nomads.