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|Ab urbe condita||1797|
|Balinese saka calendar||965–966|
|English Regnal year||N/A|
|Chinese calendar||癸未年 (Water Goat)|
3740 or 3680
— to —
甲申年 (Wood Monkey)
3741 or 3681
|- Vikram Samvat||1100–1101|
|- Shaka Samvat||965–966|
|- Kali Yuga||4144–4145|
|Japanese calendar||Chōkyū 5 / Kantoku 1|
|Minguo calendar||868 before ROC|
|Seleucid era||1355/1356 AG|
|Thai solar calendar||1586–1587|
1170 or 789 or 17
— to —
1171 or 790 or 18
|Wikimedia Commons has media related to 1044.|
- July 6 – Battle of Ménfő: German troops under King Henry III (the Black) defeat the Hungarian army led by King Samuel Aba who flees the field, but is captured and killed. Peter Orseolo (called the Venetian) becomes (for the second time) king of Hungary and a vassal of the Holy Roman Empire.
- Summer – Geoffrey II (the Hammer), count of Anjou, captures the city of Tours and takes control of the county of Touraine.
- The Chinese military treatise of the Wujing Zongyao is written and compiled by scholars Zeng Gongliang (曾公亮), Ding Du (丁度), and Yang Weide (楊惟德), during the Song Dynasty. It is the first book in history to include formulas for gunpowder, and its use for various bombs (thrown by sling or trebuchet catapult). It also describes the double-piston pump flamethrower and a thermoremanence compass, a few decades before Shen Kuo wrote of the first known magnetic mariner's compass. Although emphasizing the importance of many weapons, it reserves high respect for the crossbow, and the ability of crossbowmen to fell charging units of nomadic cavalrymen.
- August 11 – King Anawrahta seizes the throne of the Pagan Empire at Bagan in Burma (modern Myanmar).
- January 14 – Adelaide I, abbess of Quedlinburg
- April 19 – Gothelo I (or Gozelo), duke of Lorraine
- July 6 – Samuel Aba, palatine and king of Hungary
- August 11 – Sokkate, king of the Pagan Empire (b. 1001)
- November 14 – Thietmar of Hildesheim, German bishop
- Abu'l-Husayn al-Basri, Mu'tazilite faqih and theologian
- Rajendra Chola I, emperor of the Chola Dynasty
- Sharif al-Murtaza, Buyid Shia scholar (b. 965)
- Zhao Yuanyan, prince of the Song Dynasty (b. 985)