By Kevin Connolly
Northern Ireland correspondent, BBC News
Every British prime minister of modern times has ended up dealing to some extent with "the Irish question", usually because political violence has forced it on to their agenda.
The Agreement was signed in Mr Blair's first year at Downing Street
The tone of their engagement has usually been reluctant, if not downright resentful.
Politicians are bound to be suspicious of the demands of an issue where there are few, if any, British votes to be had, and whose roots stretch back to the reign of Henry II, who died in 1184.
From his earliest days in office, though, Tony Blair was different.
True, he was building on the work of his predecessor, John Major, who had opened secret negotiations with the IRA, but Mr Blair's engagement was to prove both longer and deeper.
It was enormously significant for a man with his subtle understanding of the power of symbolism that Mr Blair's first trip outside London as prime minister was to Belfast.
The depth of his commitment to the search for a stable settlement in Northern Ireland was never to waver.
Even when the other demands of office appeared almost overwhelming, time was always made for talks with Northern Ireland's often fractious and intransigent political leaders.
It's almost certain that the key players like Gerry Adams, David Trimble and latterly Ian Paisley have found it easier over the years to arrange access to Mr Blair than many of the party colleagues who've served in his Cabinets.
Part of Tony Blair's "legacy" has been the return of devolution
Even though it took him a decade to persuade Northern Ireland's politicians to work with each other, they all seemed to find it easy to work with him.
He was on first-name terms with the leaders of Republicanism, Gerry Adams and Martin McGuinness.
He was reputed to have exchanged spiritual text messages by mobile phone with the Reverend Ian Paisley.
Even the prickly Ulster Unionist David Trimble appeared, on balance, to like him.
Mr Blair's ability to appear to empathise with any negotiating partner of the moment did, however, alienate Seamus Mallon - the former deputy leader of the moderate Nationalist SDLP - who spoke of the prime minister's readiness to "buy anybody [and] sell anybody".
You hear relatively few such sour notes in the general assessment of Tony Blair on this side of the Irish Sea, perhaps because in one of the few public speeches where he touched on his motives for involving himself so deeply in Irish affairs, he told the Dail in Dublin that he "had Ireland in his blood".
He spoke of family holidays in County Donegal near where his mother was born, of learning to swim the cold Atlantic waters off Rossnowlagh, and of drinking his first Guinness in the company of his dad.
That kind of sentimentalism wouldn't have hurt his general image in Ireland but the process of cutting a deal and making it stick would take more subtle political skills.
Members of Sinn Fein travelled to Downing Street in December 1997
Mr Blair came into office in 1997 a few months after the IRA abandoned the ceasefire it had declared in 1994.
His readiness to meet the leadership of Sinn Fein, the Republican movement's political wing, saw the ceasefire swiftly restored.
It is easy to forget now, in the days when visits to 10 Downing Street by Sinn Fein delegations are so routine, that they rate only cursory mentions in Northern Ireland's local news, and that Mr Blair's first such meeting, in December 1997, was an act of real political courage.
No British prime minister since David Lloyd George in the early 1920s had met the Sinn Fein leadership.
And the meeting took place in the Cabinet Room, precisely where, in 1991, mortars fired by the IRA had landed in Downing Street, in an attempt to murder the Cabinet.
The Good Friday Agreement was signed less than year after Tony Blair entered Downing Street.
It was a distillation of his strategy for balancing the contradictory concerns of Unionism and Nationalism - assuring Protestants that Northern Ireland was safe within the United Kingdom, but simultaneously wooing Catholics with the promise that they could work for a united Ireland, as long as their means were peaceful and political.
The deal was not a final settlement - far from it.
The assembly's 108 representatives meet at the Stormont Parliament
Almost to his very last day in office, Tony Blair immersed himself in detailed talks with Northern Ireland's fractious and intransigent parties about the precise terms on which power might be shared.
Often the peace process seemed to be lurching from crisis to crisis with only the prime minister's energy and optimism to sustain it.
It was not all plain sailing - his readiness to allow Republicans into government before they'd disarmed helped to destroy the moderate UUP Unionist party, which was part of that deal.
We won't hear Mr Blair's justification for the way he handled the process until he writes his memoirs, but he would be entitled to argue that the end - stable, peaceful, power-sharing government between old enemies - justified the means.
All along, even when the IRA appeared to be dragging its heels on the issue of weapons decommissioning, Mr Blair acted as though he was sure of the good intentions of the Republican leadership.
That may have been in part because of what he was hearing from his intelligence officials, but it's also at least in part because he was backing his own first-hand judgement of the sincerity of men like Mr Adams and Mr McGuinness.
The process was so protracted we came to take it for granted, but again when you consider how the British establishment for years treated such men as mortal enemies, it's worth noting the courage it took to establish that kind of relationship.
In the end, Mr Blair's belief that an historic deal was within reach, proved right - if only just.
The historic enemies of Republicanism and Unionism finally agreed to share power just a few weeks before the end of his prime ministerial term.
They still have little in common but they all seemed keen to deliver a deal on Tony Blair's watch - and a great deal of the pressure on the parties from London in the last few months has been designed to focus them on the objective of securing this aspect of the Blair "legacy".
And what was the motivation for it all?
It would be foolish to allow the automatic scepticism of our age to blind us to the possibility that Tony Blair simply saw that there was good to be done in Ireland, and committed himself to doing it.
But there's no doubt that he's aware that playing a significant role in resolving a conflict that stretches back to the early Plantagenets will assure him of a place in the kind of history books that record the doings of statesmen, rather than the duller, more forgettable political science texts which record the duller doings of government.
And of course any assessment of Tony Blair which dwells critically on the role he played in miring Britain in the chaos of post-Sadaam Iraq will have to balance that view with the undoubted truth that in Ireland he was a builder of peace - and one who often showed considerable wisdom and patience.