|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 the Christmas.
- 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.
- 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