Byzantine Empire

• September 18 – Battle of Kapetron: A combined Byzantine-Georgian army, under Byzantine generals Aaronios and Katakalon Kekaumenos (supported by the Georgian duke Liparit IV), confronts the invading Seljuk Turks, led by Ibrahim Inal (a half-brother of Sultan Tughril), at Kapetron (near modern-day Pasinler). The Byzantines defeat their opposing Turkish forces in the flanks, but in the centre Ibrahim Inal captures Liparit, and can safely withdraw from Byzantine territory, laden with spoils and captives, including Liparit.^[1]
• Winter – Emperor Constantine IX sends an embassy with gifts and a ransom, to release Liparit IV to Tughril. However, the sultan sets Liparit free, on the condition that he will never again fight the Seljuks.

Europe

• Winter – Emperor Henry III (the Black) appoints his cousin, Bishop Bruno of Toul (related to the counts of Egisheim-Dagsburg in Upper Alsace), as successor of Damasus II at an assembly at Worms.
• The city of Oslo is founded by King Harald III (Hardrada) of Norway (approximate date).^[2]

England

• 1048 or 1066 – End of the Viking Age: Vikings make an unsuccessful raid on the Kingdom of England; The raiders flee to Flanders (modern Belgium).^[3]
• King Edward the Confessor goes to war against Flanders, blockading the English Channel with a fleet based at Sandwich in Kent.^[3]

China

• Catastrophic Yellow River flood in Northern Song China, river changes its course until 1194.

Religion

• July 16 – At orders of Henry III, German troops under Boniface III (Canossa), enter Rome and expel Pope Benedict IX.
• July 17 – Pope Damasus II succeeds Benedict IX as the 151st pope of the Catholic Church, but he dies after 23 days.

• December – Bruno von Egisheim-Dagsburg, bishop of Toul, is selected as the new pope by an assembly at Worms - after canonical election in Rome next February, he assumed the name Leo IX.