What happened in 681? — events across the world

Central Asian steppe

Muslim conquest of Transoxiana
673–751Transoxiana
In the 7th and 8th centuries, Arab armies of the Umayyad and Abbasid caliphates conquered Transoxiana in Central Asia. The region lies between the Syr Darya and Amu Darya rivers, covering parts of modern Uzbekistan, Tajikistan, Kazakhstan, and Kyrgyzstan.
SourcesWikipedia ↗
Tang campaigns against the Western Turks
640–712Central Asia
A series of military campaigns conducted by the Tang dynasty against the Western Turkic Khaganate in the 7th century. The conflicts began with Tang interventions in the rivalry between the Eastern and Western Turks to weaken both. Under Emperor Taizong, campaigns were dispatched in the Western Regions against Gaochang in 640, Karasahr in 644 and 648, and Kucha in 648.
SourcesWikipedia ↗

Founding of the Tang Dynasty
618–907Chang'an (Tang capital site), Xi'an, Shaanxi, China
The Tang dynasty was founded by Li Yuan in 618, replacing the Sui dynasty. It became a major unified dynasty in Chinese history, with its capital at Chang'an.
SourcesWikipedia ↗
Taika Reform
645–894Naniwa-kyō (Naniwa Palace site), Osaka, Japan
In 645, Emperor Kōtoku of Japan enacted the Taika Reforms, aiming to abolish clan rule and establish a centralized state modeled on Tang China, profoundly impacting Japanese history.
SourcesWikipedia ↗

Second Tikal–Calakmul War
648–695Petén Department
The Second Tikal–Calakmul War, fought from 648 to 695, was the second in a series of conflicts between Tikal and Calakmul, two of the most prosperous Maya cities in the Petén region during the Classic period. The war reflected the rivalry between major Maya city-states, and both cities were later abandoned amid the broader decline of Maya civilization.
SourcesWikipedia ↗

Convocation of the Third Council of Constantinople
680–681
The Third Council of Constantinople, convened from 680 to 681 in Constantinople, is recognized as the Sixth Ecumenical Council by the Eastern Orthodox, Catholic, and certain other Western Churches. It condemned monoenergism and monothelitism as heretical and affirmed that Jesus Christ possesses two energies and two wills.
SourcesWikipedia ↗

Muslim conquest of the Maghreb
647–709Maghreb
The Arab Empire began the conquest of the Maghreb in 647, and by 698 Carthage fell, ending Byzantine presence. By 709 the conquest of Algeria and Morocco was completed, and mass Islamization of Berbers was initiated, setting the stage for the 711 conquest of Iberia.
SourcesWikipedia ↗

Arab conquest of Armenia
642–744Greater Armenia
The Arab conquest of Armenia was a series of military campaigns launched in the mid-7th century by the Islamic polity of the Arabian Peninsula against the Byzantine-controlled region of Armenia, as part of the early Muslim conquests and the Arab–Byzantine wars.
SourcesWikipedia ↗

These are known only to the century, not to the year. They are listed separately so a rough date is never mistaken for an exact one.