Medieval kingdom in what is now modern-day northern England, from the Humber estuary north, minus Cumbria. At times, it included parts of modern southeast Scotland, up to the Edinburgh area

Dewyr, the area just north of the Humber Estuary, was settled by Angles, who called it Deira.  The Welsh kingdon of Bryneich (the eastern coast of Great Britain from the Tyne north into Scotland) was conquered by the Angles led by Ida, who named it Bernicia, centered at Bamburgh.  Between them lay the Welsh kingdom of Ebrauc, but in 580, Ælle of Deira killed the rulers of Ebrauc, the brothers Gwrgi and Peredyr, and made Eoforwic his capital.

Aneurin, along with having made several helpful suggestions for this writeup, has noded every king in the list below.

• Æthelfrith's (593-616) father Æthelric had seized the throne of Deira and driven Ælle's son Edwin into exile in Gwynedd. Æthelfrith acquired Bernicia in 593, fought the Scots to a standstill and defeated an invading army from Gwynedd seeking to put Edwin on the throne. Edwin fled to Rædwald of East Anglia. Æthelfrith attempted to bribe Rædwald to kill Edwin, but Rædwald invaded Northumbria instead, and Æthelfrith died at the Battle of the River Idle.
• St. Edwin (616-632) became bretwalda after Rædwald's death. He is slain fighting an alliance between Penda of Mercia and Cadwallon ap Capfan of Gwynedd.
• Æthelfrith's three sons lived in exile among the Scots until Edwin's death. Upon their return, two of them renounced Christianity and divided Northumbria between them:
  • Bernicia - Eanfrith (633-634)'s apostasy didn't help him against Cadwallon, who killed him during a peace parley.
  • Deira
  - Osric (633-634) had to lay siege to his own capital in 634, as Cadwallon held it. Cadwallon broke the siege and won the battle.
• Cadwallon ap Cadfan (634) according to Bede did his best to ethnically cleanse Northumbria, but was himself killed at the Battle of the Wall by
• St. Oswald (634-642), Æthelfrith's last remaining son. He eventually became bretwalda but was in turn killed by Penda of Mercia.
• Oswiu (642-670) had to share power in Deira for a while:
  • St. Oswine (644-651) soon fell out with Oswiu but went into hiding after realizing he couldn't defeat Oswiu's armies. He was found.
  • Æthelwald (651-655)
  • Alchfrid 655-, son of Oswiu.
  In 655, Oswiu won the Battle of Winwaed Field, during which Penda of Mercia and Æthelhere of East Anglia were killed. Oswiu was now bretwalda but lost Mercia to the revolt of Wulfhere in 658.
• Ecgfrith (670-685) conquered Lindsey from Wulfhere, then lost it again.
• Aldfrith (685-704)
• Osred I (705-716)
• Coenred (716-718)
• Osric (718-729)
• Ceolwulf (729-637)
• Eadbert (737-758)
• Oswulf (758-759)
• Oswin (759-761)
• Æthelwald Moll (761-765)
• Alhred (765-774)
• Æthelred Moll (774-778)
• Ælfwald (778-788)
• Osred II (789-790)
• Æthelred Moll (790-796)
• Eardwulf (795-806)
• Ælfwald II (806-807)
• (St.) Eardwulf (808)
• Eanred (808-840)
• Æthelred II (840-844)
• Rædwulf (844)
• Æthelred II (844-848)
• Osberht (848-863)
• Ælle II (863-867)'s squabbles with Osberht weakend Northumbria at a critical time, when Viking incursions from Dublin reached their greatest.

The Viking kingdom of Dublin served as a base for Viking invasions of Northumbria. In 865, the brothers Halfdan, Hubba, and Ivarr the Boneless captured part of East Anglia; they pushed into Northumbria by 866. Aelle and Osberht patched up their differences but it was too late; they were killed fighting together in 867, followed by a sack of York which ended Northumbria for good.

For the next 80 years or so, descendants of Ivarr and Halfdan ruled the northern part of England from York, now called Jorvik (follow the link). The Kingdom of Jorvik appears to have had about the same extent as the old kingdom of Deira; the earls of Bernicia appear to have had some measure of independence.

The Anglo-Saxons remaining in the south still called the area "Northumbria" of course, and certainly never gave up the idea of reconquering it. This came to pass in 927 when Aethelstan of Wessex expelled king Guthfrith from York. Aethelstan ruled most of England until his death in 939, after which things began to come apart again. The 940's are extremely complicated, with several cycles of mostly-Viking-descended Northumbrians electing Viking kings and an Anglo-Saxon king riding north to expel them time after time; I've left these under Jorvik for now.

Northumbria was permanently united with the rest of England in the year 954, when Eric Bloodaxe was killed, and Eadred of Wessex resumed overlordship. A brief interlude of rebellion against Eadred's successor Eadwig replaced him with his own brother Edgar, who inherited the lot in 959 anyway. For what happened later, see Rulers of England. The area was subject to uprisings and Viking invasions until the Battle of Stamford Bridge in 1066.

Pieced together from
http://family-of-man.com/CatalogEnglish/Europe/Ancient_Europe/saxons_britons.html
http://www.stephen.j.murray.btinternet.co.uk/northumbria.htm
http://www.asnc.cam.ac.uk/pase/Level1/Level2/Rulers.html