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|Ab urbe condita||1790|
|Balinese saka calendar||958–959|
|English Regnal year||N/A|
|Chinese calendar||丙子年 (Fire Rat)|
3733 or 3673
— to —
丁丑年 (Fire Ox)
3734 or 3674
|- Vikram Samvat||1093–1094|
|- Shaka Samvat||958–959|
|- Kali Yuga||4137–4138|
|Japanese calendar||Chōgen 10 / Chōryaku 1|
|Minguo calendar||875 before ROC|
|Seleucid era||1348/1349 AG|
|Thai solar calendar||1579–1580|
1163 or 782 or 10
— to —
1164 or 783 or 11
|Wikimedia Commons has media related to 1037.|
- Spring – A revolt in northern Italy is started by Archbishop Aribert of Milan. King Henry III (eldest son of Emperor Conrad II) travels south of the Alps to quell it.
- February – At an Imperial Diet in Pavia (assembled by Conrad II), Aribert is accused of fomenting a revolt against the Holy Roman Empire, Conrad orders his arrest.
- May – Conrad II, with Pavian assistance, lays siege to Milan at the Porta Romana side, but the city holds out. In Rome, Pope Benedict IX deposes Aribert as archbishop.
- May 28 – Conrad II decrees the Constitutio de Feudis which protects the rights of the valvassores (knights and burghers of the cities) in Lombardia (modern Italy).
- Summer – A Byzantine expeditionary force under George Maniakes lands at Sicily, and defeats the Zirids. Maniakes begins his campaign to reconquer the island.
- September 4 – Battle of Tamarón: Ferdinand I defeats and kills his brother-in-law Bermudo III. Ferdinand becomes the king of Castile and León (modern Spain).
- King Harold I seizes the throne of England from his half-brother Harthacnut. His mother, Emma of Normandy flees to Bruges in Flanders (modern Belgium).
- September 4 – Bermudo III (or Vermudo), king of León
- November 15 – Odo II, French nobleman (b. 983)
- Abu'l-Hasan Mihyar al-Daylami, Persian poet
- Abu Mansur al-Baghdadi, Persian Shafi'i scholar
- Baba Kuhi of Shiraz, Persian Sufi mystic (b. 948)
- Avicenna, Persian physician and polymath (b. 980)
- Boleslaus III (the Red), duke of Bohemia
- Ding Wei, grand chancellor of the Song Dynasty
- Farrukhi Sistani, Persian poet (or 1038)
- John of Debar, Bulgarian clergyman and bishop
- Muhammad al-Baghdadi, Persian mathematician
- Muirgeas ua Cú Ceanainn, king of Uí Díarmata
- Robert II, French prelate and archbishop
- Siegfried II, German nobleman (b. 956)
- William III (Taillefer), French nobleman