Background

Medieval Ireland's most famous king, Brian Boru, c.941-1014, belonged to the Dál Cais dynasty whose main royal stronghold was just north of the town of Limerick at Kincora, Cenn Corad, which is now Killaloe, Co. Clare.  Although the Dál Cais were not particularly powerful to begin with, Brian built on the successes of his father, Cennétig, and particularly his older brother, Mathgamain, to make himself overking of all the various Munster kingdoms, and later to seize the high-kingship of Ireland. 

The family-tree below sets out the Dál Cais' extensive dynasty with Brian, his brother Mathgamain, and his father Cennétig circled:

Table from Seán Duffy, Brian Boru and the Battle of Clontarf (Dublin, 2013), p. 63.

Brian was one of twelve sons, and as a younger son was not expected to become king. His own family was also extensive. Offspring, in the Middle Ages, were often used to make politically advantagous marraiges, and Brian's many sons and daughters were no different.  As can be seen from the tree below, many of Brian's daughters were married off to important rivals in order to create or cement political alliances - a practice which was not always sucessful. 

One example of this political match-making can be seen in the marraige of Brian's daughter Sadb to the son of Máel Muad, the man who was responsible for the slaughter of Brian's older brother, Mathgamain. 

Table in Seán Duffy, Brian Boru and the Battle of Clontarf, (Dublin, 2013), p. 100.

From Overlord of Munster to the Emperor of the Irish

Brian spent many years extending his influence and authority over neighbouring kings, including the Viking rulers of Limerick and Waterford, and he compiled an impressive army and navy.

Once confident of his dominance in Munster, Brian Boru began to extend his control, putting pressure on the kings of Osraige and Leinster to the east, eventually winning their submission. A major part of his career was dedicated to increasing the pressure on the high-king of Ireland, Máel Sechnaill, whose Uí Néill dynasty had held the high-kingship unopposed for centuries.

It was only after Brian's capture of Viking Dublin in 999, that Máel Sechnaill reluctantly acknowledged Brian Boru as the most powerful king in Ireland. Many years of military campaigning followed as Brian sought, and eventually received, the submission of every other major king in the north. He was now described in one source, with some accuracy, as 'Emperor of the Irish'.

Rebellion and Legacy

This control, however, was fleeting and it was not long before some of those kings who had submitted to Brian began to rebel.  Facing an alliance of the Dublin Vikings, their Leinster allies and other Vikings recruited from overseas, Brian Boru, likely in his early 70s, was eventually killed at the Battle of Clontarf near Dublin in April 1014.

National Library of Ireland

His rise to power had been extraordinary, and Brian quickly became a legendary figure in Irish history. His reign was romanticised as the descendants of Brian, the Uí Briain, commissioned works such as the Cogadh Gáedhel re Gallaibh, 'The War of the Irish Against the Foreigners', a colourful, partisan text portraying him as Ireland's saviour from the pagan Vikings.

This mixture of history and legend was hugely influential in shaping the subsequent impression of Brian Boru and ensuring that a positive and heroic memory of this medieval king endured.  

Sources: 

Francis John Byrne, Irish Kings and High Kings (Dublin, 2001).

Anthony Candon, 'Muirchertach Ua Briain: Politics and Naval Activity in the Irish Sea' in Gearóid Mac Niocaill and Patrick F. Wallace (eds), Keimelia: Studies in Medieval Archaeology and History in Memory of Tom Delaney (Galway, 1988), pp 397-415.

Máire Ní Mhaonaigh, 'Bréifne Bias in Cogad Gáedel re Gallaib' in Ériu Vol. 43 (Jan 01, 1992), pp 135-158.

Máire Ní Mhaonaigh, Brian Boru: Ireland’s Greatest King? (Stroud, 2007).

Máire Ní Mhaonaigh, 'Cogad Gáedel Re Gallaib' and the Annals: A Comparison' Ériu Vol. 47 (Jan 01, 1996), pp 101-126.

Dáibhí Ó Cróinín, Medieval Ireland 400-1200, (Essex,1995).

John Ryan, 'Brian Boruma, King of Ireland' in Etienne Rynne (ed), North Munster Studies: Essays in Commemoration of Monsignor Michael Moloney, (Limerick, 1967), pp 355-374.

James Henthorn Todd, (ed.), intro. and trans. Cogadh Gaedhel re Gallaibh = The war of the Gaedhil with the Gaill, or, The invasions of Ireland by the Danes and other Norsemen (London,1867).

Trivia: 
The first name Brian is of Breton origin and was not common in Ireland before Brian Boru.