|Ab urbe condita||1774|
|Balinese saka calendar||942–943|
|English Regnal year||N/A|
|Chinese calendar||庚申年 (Metal Monkey)|
3717 or 3657
— to —
辛酉年 (Metal Rooster)
3718 or 3658
|- Vikram Samvat||1077–1078|
|- Shaka Samvat||942–943|
|- Kali Yuga||4121–4122|
|Japanese calendar||Kannin 5 / Jian 1|
|Minguo calendar||891 before ROC|
|Seleucid era||1332/1333 AG|
|Thai solar calendar||1563–1564|
1147 or 766 or −6
— to —
1148 or 767 or −5
|Wikimedia Commons has media related to 1021.|
- November – Emperor Henry II conducts his fourth Italian military campaign. He crosses the Brenner Pass with a 60,000-strong army, and reaches Verona, where he receives Lombard levies. Henry proceeds to Mantua and then into Ravenna, to spend Christmas there.
- The Taifa of Valencia, a Moorish kingdom in Al-Andalus (modern Spain), becomes independent from the Caliphate of Córdoba (approximate date).
- Senekerim-Hovhannes Artsruni, king of Vaspurakan (Greater Armenia), surrenders his kingdom to the Byzantine Empire. He receives in return Sebasteia and becomes governor of Cappadocia.
- Hovhannes-Smbat III, King of the Armenian kingdom of Ani was attacked by his younger brother Ashot IV, and lost much of his power to him, becoming concurrent king of outlying territories.
- The Chinese capital city of Kaifeng has some half a million residents by this year; including all those present in the nine designated suburbs, the population is over a million people.
- Emperor Rajendra Chola I extends his influence of the Chola Empire to the banks of the Ganges River (North India) and invades Bengal.
- Sultan Mahmud of Ghazni appoints Malik Ayaz to the throne, making Lahore (modern Pakistan) the capital of the Ghaznavid Empire.
- February 13 – Al-Hakim bi-Amr Allah, Fatimid caliph (b. 985)
- March 16 – Heribert, archbishop of Cologne (b. c. 970)
- July 7 – Fujiwara no Akimitsu, Japanese bureaucrat (b. 944)
- August 17 – Erkanbald, German abbot and archbishop
- August 29 – Minamoto no Yorimitsu, Japanese nobleman (b. 948)
- Arnulf, French archbishop and illegitimate son of Lothair III
- Fujiwara no Yoshikane, Japanese nobleman (b. 957)
- Hamid al-Din al-Kirmani, Fatimid scholar and philosopher
- Hamza ibn 'Ali ibn-Ahmad, founding leader of the Druze
- Liu Mei, Chinese official and general (approximate date)
- Mac Cú Ceanain, king of Uí Díarmata (Ireland)
- Shams al-Dawla, Buyid emir of Hamadan (Iran)
- Trilochanapala, king of the Kabul Shani Dynasty