|Centuries:||3rd century – 4th century – 5th century|
|Decades:||300s 310s 320s – 330s – 340s 350s 360s|
|Years:||334 335 336 – 337 – 338 339 340|
|337 by topic|
|State leaders – Sovereign states|
|Birth and death categories|
|Births – Deaths|
|Establishment and disestablishment categories|
|Establishments – Disestablishments|
|Ab urbe condita||1090|
|Chinese calendar||丙申年 (Fire Monkey)
3033 or 2973
— to —
丁酉年 (Fire Rooster)
3034 or 2974
|- Vikram Samvat||393–394|
|- Shaka Samvat||259–260|
|- Kali Yuga||3438–3439|
|Iranian calendar||285 BP – 284 BP|
|Islamic calendar||294 BH – 293 BH|
|Minguo calendar||1575 before ROC
|Seleucid era||648/649 AG|
|Thai solar calendar||879–880|
Year 337 (CCCXXXVII) was a common year starting on Saturday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Felicianus and Titianus (or, less frequently, year 1090 Ab urbe condita). The denomination 337 for this year has been used since the early medieval period, when the Anno Domini calendar era became the prevalent method in Europe for naming years.
- May 22 – Constantine the Great, first Christian Roman emperor of the Western Empire (312–324), and of the Roman Empire (324–337), dies in Achyron, near Nicomedia, at age 65 after he is baptized by Eusebius of Nicomedia.
- September 9 – Constantine II, Constantius II, and Constans succeed their father Constantine I as co-emperors. The Roman Empire is divided between the three Augusti (see map).
- September – A number of descendants of Constantius Chlorus, and officials of the Roman Empire, are executed for a purge against the sons of Constantine I.
- King Shapur II of Persia begins a war against the Roman Empire. He sends his troops across the Tigris to recover Armenia and Mesopotamia.
- Shapur II besieges the Roman fortress of Nisibis (Syria), but is repulsed by the forces under Lucilianus.
- February 6 – A 4-month papal vacancy ends. Pope Julius I succeeds Pope Mark as the 35th pope.
- June 17 – Constantius II announces the restoration of Athanasius as Patriarch of Alexandria.
- Paul I becomes Patriarch of Constantinople.
- Faxian, Chinese Buddhist monk and traveler (approximate date)
- Fú Jiān, emperor of the Chinese Di state Former Qin (d. 385)
- Lü Guang, founding emperor of the Di state Later Liang (d. 400)
- Zenobius of Florence (d. 417)
- Alexander of Constantinople
- May 22 – Constantine the Great, first Christian Emperor of the Roman Empire (b. 272)
- Eustathius of Antioch (approximate date)