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.
• Abd al-Aziz al-Mansur, a grandson of the prominent Andalusian figure Almanzor begins his rule in Taifa of Valencia, a Moorish kingdom in Al-Andalus (modern Spain), ushering in a period of relative stability and prosperity that will last until 1061. Taifa of Valencia gained its independence from the Caliphate of Córdoba in 1010.

• February 13 – On one of his habitual night rides in the outskirts of Cairo, the Fatimid caliph al-Hakim bi-Amr Allah disappears, most likely assassinated by disaffected palace factions, apparently involving his sister, Sitt al-Mulk.{{cite book | last=Halm | first=Heinz | author-link=Heinz Halm | title=Die Kalifen von Kairo: Die Fāṭimiden in Ägypten, 973–1074 | language=de | trans-title=The Caliphs of Cairo: The Fatimids in Egypt, 973–1074 | publisher=C. H. Beck | location=Munich | year=2003 | isbn=3-406-48654-1 | url={{Google Books|Hj2bhVntO3EC|plainurl=yes}} | pages=297–302}}
• March 26 – On the feast of Eid al-Adha, the death of al-Hakim, kept secret for six weeks, is announced, along with the succession of his son, al-Zahir li-i'zaz Din Allah. On the same day, al-Hakim's designated heir, Abd al-Rahim ibn Ilyas, is arrested in Damascus and brought to Egypt.{{cite book | last=Halm | first=Heinz | title=Die Kalifen von Kairo: Die Fāṭimiden in Ägypten, 973–1074 | language=de | trans-title=The Caliphs of Cairo: The Fatimids in Egypt, 973–1074 | publisher=C. H. Beck | location=Munich | year=2003 | isbn=3-406-48654-1 | url={{Google Books|Hj2bhVntO3EC|plainurl=yes}} | pages=307–308}}
• The last evidence of indigenous Christian and non-Arabophone culture in Tripolitania (modern Libya) is seen.{{vague|date=February 2021}}{{cite book|last=Bresc|first=Henri|title=Parte prima. Il regno normanno e il Mediterraneo|chapter=La Sicile et l'espace libyen au Moyen Age|year=2003|chapter-url=http://www.storiamediterranea.it/public/md1_dir/b1462.pdf |archive-url=https://ghostarchive.org/archive/20221009/http://www.storiamediterranea.it/public/md1_dir/b1462.pdf |archive-date=2022-10-09 |url-status=live|accessdate=January 17, 2012}}

• Senekerim-Hovhannes Artsruni, king of Vaspurakan (Greater Armenia), surrenders his kingdom to the Byzantine Empire. In return, he receives Sebasteia and becomes governor of Cappadocia.{{cite book | last = Hewsen | first = Robert H. | title = Armenia: A Historical Atlas | year = 2001 | publisher = The University of Chicago Press | isbn = 0-226-33228-4 | page = 126}}
• Battle of Shirimni, the Byzantine Empire under Basil II defeats the Kingdom of Georgia under Giorgi I at Shirimni, at the Lake Palakazio, modern Lake Çıldır, Turkey
• Hovhannes-Smbat III, King of the Armenian kingdom of Ani, is attacked by his younger brother Ashot IV, and loses much power to him, becoming concurrent king of outlying territories.
• 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.
• 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.

• Vikings known to be occupying L'Anse aux Meadows on Newfoundland (island).Based on dating of a felled tree using dendrochronology based on a timeline using the 993–994 carbon-14 spike. {{Cite journal|last1=Kuitems|first1=Margot|last2=Wallace|first2=Birgitta L.|last3=Lindsay|first3=Charles|last4=Scifo|first4=Andrea|last5=Doeve|first5=Petra|last6=Jenkins|first6=Kevin|last7=Lindauer|first7=Susanne|last8=Erdil|first8=Pınar|last9=Ledger|first9=Paul M.|last10=Forbes|first10=Véronique|last11=Vermeeren|first11=Caroline|date=October 20, 2021|title=Evidence for European presence in the Americas in ad 1021|journal=Nature|volume=601 |issue=7893 |pages=388–391|doi=10.1038/s41586-021-03972-8|pmid=34671168|pmc=8770119 |s2cid=239051036|issn=1476-4687|quote=Our result of AD 1021 for the cutting year constitutes the only secure calendar date for the presence of Europeans across the Atlantic before the voyages of Columbus [in 1492]. Moreover, the fact that our results, on three different trees, converge on the same year is notable and unexpected. This coincidence strongly suggests Norse activity at L’Anse aux Meadows in AD 1021.|doi-access=free}}

• December 8 – Wang Anshi, Chinese chancellor (d. 1086)
• Eudokia Makrembolitissa, Byzantine empress (d. 1096)
• Fujiwara no Kanshi, Japanese empress consort (d. 1102)
• Wugunai, Chinese chieftain of the Wanyan tribe (d. 1074)

• February 13 – Al-Hakim bi-Amr Allah, Fatimid caliph (b. 985)
• March 5 – Arnulf, French archbishop and illegitimate son of Lothair III
• 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)
• 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

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